# Do Enceladus' geysers fall back to its surface or do they achieve escape velocity?

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Enceladus, a moon of Saturn, has a very low surface gravity at 0.114 m/s² or 0.012 g. It has a subsurface ocean of liquid water and is ejecting plumes of it. Does the ejected water eventually fall/rain down to the surface or does it (or some of it) achieve escape velocity due to Enceladus' very low mass and gravity? If so, is Enceladus losing mass and will eventually run out of water?

We start by calculating the moon Enceladus surface escape velocity $$v_e$$ as $$v_e=sqrt{frac{2GM}{r}}$$ where $$G = 6.674×10^{-11}m^3kg^{-1}s^{-2}$$ is the universal gravitational constant, $$M=1.08×10^{20}kg$$ is the moon mass, and $$r=2.52×10^5m$$ is the radius of the moon. Evaluation of the above equation gives us an escape velocity of about $$239m/s$$.

Perry et al. provide high fidelity observations of Enceladus vapor plumes from the Cassini spacecraft.

The above graph is just for the high velocity plumes as described in the paper:

The H2O neutrals measured during E8 had a Mach-4 distribution centered on 1.2 km/s with a width of ±300 m/s, which corresponds to a temperature of 65K

Since the average high speed plume velocity of 1.2km/s is about five times greater than our calculated escape velocity of 239m/s, we can conclude that some of Enceladus's plumes certainly achieve escape velocity.

Teolis et al. agree:

The expression assumes radial expansion of the gas from the surface sources at constant speed, neglecting gravity since the mean molecular speed in the jets significantly exceeds (by at least a factor two) the 240 m/s Enceladus escape speed.

Enceladus is losing mass through it's (mostly water) jets. I couldn't find a conclusive analysis of mass loss rate. Eventually I would expect that enough water will be lost that the current mechanism for creating the jets under the 10 km ice crust will no longer be in effect, but this is just my intuition. I don't have a credible source or calculation to back this up.

## Enceladus, the icy moon that might harbour life

Imagine a small world somewhere in the Solar System. Its surface is made of water ice, in some places &ndash smooth and shiny, in some &ndash cracked and cratered. It is always chilly here, the average temperature is about -200 degrees, and the Sun looks small and dim. But if you are standing in the right place, you can see a breathtaking sight: enormous Saturn frozen in the sky, it&rsquos rings &ndash just shadows below the planet&rsquos equator&hellip

Welcome to Enceladus, the sixth biggest moon of Saturn, the shiniest object in the Solar System, one of the few worlds with the global water ocean and a place that seems to have all the ingredients necessary to support life as we know it.

But let&rsquos start at the beginning&hellip

## 101 Geysers on Enceladus (and What They Imply)

I’ve mentioned before the irony that we may discover signs of robust extraterrestrial life sooner around a distant exoplanet than right here in our own Solar System. The scenario isn’t terribly implausible: Perhaps we come up empty on Mars, or find ourselves bogged down with ambiguous results. As our rovers dig, we still have Europa, Enceladus and other outer system possibilities, but probably face a wait of decades before we could build and fly the missions needed to identify life.

Meanwhile, the exoplanet hunt continues. While we’ve had many a setback — the Space Interferometry Mission will always stand out in this regard, not to mention the inability to follow through with Terrestrial Planet Finder, Darwin and other high-end concepts — it’s just possible that within the next few decades, a space-based observatory will detect a solid biosignature from an exoplanet’s atmosphere. Even the James Webb Space Telescope should be able to detect the transmission spectrum of an Earth-class planet transiting a dim red dwarf star. Future instruments will be able to take atmospheric characterization down to an Earth 2.0 around a Sun-like star.

Then again, maybe the outer Solar System will prove so enticing that we do decide to make it a priority. We could be seeing this happen right now. Every new piece of evidence from Cassini helps to build the case that Enceladus is an attractive proposition for the life search, the latest news being that the Saturn orbiter has identified 101 distinct geysers erupting on the moon’s surface. We first detected geysers of ice particles and water vapor at Enceladus’ south pole almost a decade ago. Now we have a map of geysers erupting from the so-called ‘tiger stripe’ fractures coincident with surface hot spots.

Image: This two-image mosaic is one of the highest resolution views acquired by Cassini during its imaging survey of the geyser basin capping the southern hemisphere of Saturn’s moon Enceladus. It clearly shows the curvilinear arrangement of geysers, erupting from the fractures. From left to right, the fractures are Alexandria, Cairo, Baghdad, and Damascus. As a result of this survey, 101 geysers were discovered: 100 have been located on one of the tiger stripes , and the three-dimensional configurations of 98 of these geysers have also been determined. The source location of the remaining geyser could not be definitively established. These results, together with those of other Cassini instruments, now strongly suggest that the geysers have their origins in the sea known to exist beneath the ice underlying the south polar terrain. Credit: NASA/JPL-Caltech/SSI.

The reason this is so exciting is that the hot spots that Cassini’s heat-sensing instruments found in the south polar region are only a few tens of meters across. That means they’re too small to be produced by the kind of frictional heating that would be caused by the repeated flexing of Enceladus due to tidal effects from Saturn. Frictional heating could have accounted for the geyser phenomena by turning surface ice into vapor and liquid, but it now appears that we’re dealing with water from the ocean below being exposed by opening and closing of the fractures.

Carolyn Porco (Space Science Institute) is leader of the Cassini imaging team, and lead author of a new paper on the Cassini findings:

“Once we had these results in hand we knew right away that heat was not causing the geysers but vice versa. It also told us the geysers are not a near-surface phenomenon but have much deeper roots.”

The source of the material forming the geysers of Enceladus is thus found to be the sea that exists under the ice shell, a sea that Cassini’s gravity data on the moon has confirmed. This news release from CICLOPS (Cassini Imaging Central Laboratory for Operations) has more, including the results of a second paper in which the authors report that the brightness of the combined geyser plume as viewed by Cassini changes periodically during the moon’s orbit of Saturn. In most respects, the brightness variations track the expected tidal venting cycle.

But not entirely. What would be expected from the opening and closing of the fractures does not predict when the plume begins to brighten, a finding that could implicate the spin rate of Enceladus. Francis Nimmo (UC-Santa Cruz) is lead author on the second paper:

“It’s an interesting puzzle. Possibilities for the mismatch include, among other effects, a delay in the response of the ice shell, which would suggest tides are heating the bulk of the ice at the south pole, or subtle changes in the spin rate of Enceladus.”

That last remark points to the possibility that the liquid water under the Enceladan ice may be global, even if deeper under the south pole region. So we have yet another reason for fascination with a moon whose salty sea, known to contain organic compounds, is spouting geysers and, possibly, reaching the surface on occasion as a liquid. We have a potentially habitable environment under the ice that periodically offers up samples to nearby spacecraft.

Enceladus is too good a target to resist, and it’s worth remembering mission concepts like Life Investigation for Enceladus (LIFE), developed by Peter Tsou. LIFE could launch in the early 2020s, reaching Saturn in 2030 with the help of gravity assists along the way, capturing material from the Enceladus geysers with an aerogel collector like the one NASA used in its Stardust comet mission. With a final gravity assist at Titan, LIFE would then bring its samples back to Earth in 2036.

I’m remembering, too, NASA astrobiologist Chris McKay’s exhortation that the venting of water and organics into space is ‘an open invitation to go there.’ The German Aerospace Center (DLR) has likewise been exploring Enceladus mission concepts, envisioning a lander that would drill through the ice. Enceladus Explorer would use an ice drill probe to melt its way into a water-bearing crevasse to look for microorganisms, on the theory that any life in the plumes would have been destroyed by sudden exposure to space. Thus the need to probe the ocean itself.

So the ideas for sampling Enceladus for life are out there and they’ll doubtless increase as Cassini continues to demonstrate how potent an astrobiological target this moon is. Which concept should we choose, and for that matter, which should we choose between Enceladus and Europa in terms of life-seeking mission destinations for spacecraft that can be flown in the near future? Both have legitimate claims on our attention, and the possibility of plumes on Europa itself (see Water Vapor Detected Above Europa) may change the equation. Will these enticing moons motivate us to reach them before a near-term space telescope finds the first biosignatures around an exoplanet?

The papers are Porco et al., “How the Geysers, Tidal Stresses, and Thermal Emission Across the South Polar Terrain of Enceladus are Related,” The Astronomical Journal Vol. 148, No. 3 (2014), 45 (abstract) and Nimmo et al., “Tidally Modulated Eruptions on Enceladus: Cassini ISS Observations and Models,” The Astronomical Journal Vol. 148, No. 3 (2014) 46 (abstract). On the LIFE mission, see Tsou et al., “LIFE: Life Investigation For Enceladus: A Sample Return Mission Concept in Search for Evidence of Life,” Astrobiology Vol. 2, No. 8 (September 12, 2012). Abstract available.

Comments on this entry are closed.

I am still trying to figure out how the liquid water ocean became established in the first place, although if there were orbital resonances in the past, or if Enceladus and her sisters periodically move in and out of resonances, that could explain it. How about the idea that… Enceladus somehow interacts with Saturn’s magnetic field electric currents get generated in the rocky-metallic core (or salty ocean) and inductive heating takes place to melt the ice? If so, could mean a lot more icy moons with liquid water oceans.

Assuming the ice surrounding the hole created by a geyser is warm enough to become slushy (and too thin or too deep to position a vehicle on it) then perhaps a simple probe, attached to a line, might be propelled from the vehicle onto this slushy area. The line would be reeled back to the vehicle while the probe scraped up slush for analysis.

Not nearly as useful as a direct probe of the internal ocean. Doing that, though, requires a crust thin enough to get a drill through.

Going back to micro sats for a moment, could a spinning cone offer a simple way for a small probe to fall into a plume with minimal effort. I’m thinking of the Benford’s spinning ablation cones in microwaves. Just substitute the plume for the microwave beam and have the cone be heavy enough to track down to the plume source. As for finding life – there are simple throwaway microscopes , e.g. Foldscope to provide unambiguous images of cellular forms, plus a host of simple molecular detectors for Earth type life. I would also consider some sort of simple lure (light?) for larger orgnisms. Send a swarm to Enceladus, and see if any strike pay dirt. The cost should be comparatively low as the probes and detection methods are almost trivially simple and basic.

I think drilling is a very difficult prospect for a space mission, seeing as it requires massive consumables and is prone to failure. Sinking a probe through miles of ice by melting requires a lot of energy, but could conceivably be achieved with a nuclear reactor or suitable radioisotope heating elements. Until such time as we are ready to develop and fly such high power nuclear technology, it seems picking up traces of organics from the geyser ejecta is the only viable approach to looking for life on Enceladus.

Microbes (if there ARE any) being destroyed in the venting process MAY turn out to be a very good thing! Cassini can get as close to the holy grail without touching it as possible. but only if we get INCREDIBLY lucky! Heres the scenario. For this to be possible, there must ALSO be a very RUDIMENTARY form of multicellular life, as well as the microbes. When this multi-celled life DECOMPOSES, Methyl Mercaptan (CH3HS) is produced. The microbes then INGEST it, and it is released into space when the microbes are distroyed. CH3SH can only* be produced by either natural BIOLOGICAL or by non-natural industrial proceces! The compound is SIMPLE enough to detect with Cassini’s spectrometer in sufficient (aye, there’s the rub). The LACK of any announcement means that, if it’s there, the amounts are too low to be conclusive. BUT: next year (if all goes well), just before Cassini enters its “Grand Finale” phase, it is scheduled to make ONE MORE PASS through the guysers, AND, it will do so at a MUCH LOWER ALTITUDE then ever before! I ,foe one, am holding my breath for any positive results! *should this near-miracle occur, expect MANY CHALLENGES to this ASSUMPTION from the scientific community.

We could nuke Enceladus from orbit to make a hole for a probe. It’s the only way to be sure. :^) Hey, a Russian scientist seriously suggested this for Europa less than a decade ago.

Behold Enceladus: Cassini Maps 101 Geysers on Tiny Saturn Moon

Saturn’s moon Enceladus is already known as one of the most intriguing places in our solar system, and now new findings from the Cassini spacecraft have been published, which will only add to our fascination with this little world.

Before Cassini, Enceladus was expected to be little more than a frozen ball of ice and rock, being so distant from the sun. But this moon held surprises, the kind which would make Enceladus a much more interesting place, and a new prime target in the search for possible life elsewhere in the solar system.

In 2005, Cassini made its first discovery of something amazing – water vapor geysers spewing out from the surface. Geysers? How could there be something like that on this tiny cold moon? But there they were since then many images have been taken and Cassini has even passed directly through some of them, sampling the spray as it did so. The plumes contained water vapor, ice particles, salts and organics. They were found to originate from deep fissures called “tiger stripes” at the south pole of the moon, which were warmer than the surrounding icy terrain. So what did this mean? Could there be water somewhere below the surface, like on Jupiter’s moon Europa? The new results presented today support that incredible idea – the fissures allow water from a subsurface sea to make its way to the surface, when then explodes out into space as huge plumes of water vapor which then freeze into ice particles.

The new findings are the result of the previous seven years of study of the geysers Cassini scientists have now produced a detailed map of the known geysers, all 101 of them! They have been published in two new papers in the online edition of The Astronomical Journal (abstract/download here).

“Once we had these results in hand, we knew right away heat was not causing the geysers, but vice versa,” said Carolyn Porco, leader of the Cassini imaging team from the Space Science Institute in Boulder, Colorado. “It also told us the geysers are not a near-surface phenomenon, but have much deeper roots,” she added. She is also the lead author of the first paper.

Mapping the locations of the plumes helped scientists to better pinpoint where they originate, which, as theorized, turned out to be below the outer icy crust of Enceladus. Pathways through the ice (the fissures) should be able to remain open, allowing liquid water from deeper inside the moon to escape to the surface. By analyzing the gravity data from Cassini, it was determined that the source of the plumes must be the subsurface sea.

See also this excellent summary of these findings on the CICLOPS website. As Carolyn Porco so eloquently summarizes:

“As we contemplate the approaching end of Cassini’s travels around Saturn, we dream of the day, hopefully not far in the future, when we can return to Enceladus to answer the question now uppermost in the mind: Could a second genesis of life have taken hold on this small icy moon of a hundred and one geysers? For we now know this: if life is indeed there, it is there for the taking.”

I agree that drilling on any icy moon is very far in the future.
However, since the geysers spray the material into space a sample
return with an aereogel like material should be possible.
A difficulty would be preserving the samples for the long return
trip. And, of course, it would be a very long mission.

It’s funny how NASA is concentrating its search of life on Mars
where they neither organic compounds nor liquid water have been

Living On The Edge – The Icy Plains Of Enceladus (part 3)

“We must believe then, that as from hence we see Saturn and Jupiter if we were in either of the Two, we should discover a great many Worlds which we perceive not and that the Universe extends so in infinitum”.

– Cyrano de Bergerac – “A Voyage to the Moon”, (1656)

In his ‘Voyage to the Moon’, which is considered one of the best examples of early science fiction, 17-century French satirist and dramatist Cyrano de Bergerac satirized the politics and religious beliefs of his day, while also contemplating an infinite Universe that was populated with an infinite number of worlds.

Taking a cue from this fictional story, NASA’s Voyager, Galileo and Cassini missions have helped to reveal more than 300 year later the true magnificence and beauty of the moon systems of all the gas giant planets in the outer Solar System, while also opening our eyes to the intriguing possibility for life on some of these fascinating worlds.

The second part of this article focused on Jupiter’s moon Europa, whose underground ocean is considered a potential cradle for life. Yet, even more equally fascinating worlds await us as we journey further out in the Solar System. Approximately a billion and a half kilometers from the Sun, two of Saturn’s 62 moons, Enceladus and Titan, are also intriguing astronomers with their potential to host potentially habitable environments as well.

Yet, the fascinating and mystifying Enceladus beckons. “As we contemplate the approaching end of Cassini’s travels around Saturn, we dream of the day, hopefully not far in the future, when we can return to Enceladus to answer the question now uppermost in the mind: Could a second genesis of life have taken hold on this small icy moon of a hundred and one geysers?” asks Porco. “For we now know this: if life is indeed there, it is there for the taking.”

The only thing that stops us from returning again to this fascinating small world in the outer Solar System, is simply our own decision not to.

## Keywords

Doctoral Candidate, Centre of Control Theory and Guidance Technology, School of Astronautics, No. 92, Dazhi W Street, Harbin, Heilongjiang, PR China currently Visiting Doctoral Student, Mechanical and Aerospace Engineering Department, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada.

Associate Professor, Mechanical and Aerospace Engineering Department, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada.

Professor, Centre of Control Theory and Guidance Technology, School of Astronautics, No. 92, Dazhi W Street, Harbin, Heilongjiang, PR China.

## How Gravity Paints a Picture

This stream does fluctuate, for Enceldaus orbits Saturn in 33 hours. Because of the elliptical orbit, Enceladus goes through tidal forces, or gravitational pull, that heats up the subsurface water. In fact, as Enceladus gets closer to Saturn the fissures from which the water vapor escapes close up and as Enceladus gets further from Saturn the fissures open up. Infrared observations gathered by the Visual and Infrared Mapping Spectrometer from 2005 to 2012 show that the plumes can increase in size by as much as 3 times their minimum and also escape at a faster velocity. Scientists suspect that the pull of gravity closes the fissures but that once the gravity is less the fissures open back up. This may also explain why the peak for emissions is 5 hours after the moon&aposs perihelion with Saturn (Johnson "Enceladus", NASA "Cassini Spacecraft," Haynes "Saturn&aposs").

## 4. ERUPTION DYNAMICS

No geyser looks or acts the same as any other. Each has its own arrangement of reservoirs and tubes, water supply, and heat source. However, by closely observing the activity of individual geysers and groups of them, it is possible to learn much concerning the general nature of operational modes.

Models of geyser dynamics from the nineteenth century and the first half of the twentieth century were mostly qualitative in the sense that they lacked quantitative fluid-dynamic and thermodynamic interpretations of empirical observations. More recent studies have used geophysical measurements, in situ measurements of pressure and temperature, video recordings, and thermomechanical models to quantify various aspects of the geysering process. We first review observational constraints for processes in the reservoirs and conduits that deliver water to the surface, and then we describe the processes that influence the visible surface eruption.

### 4.1. Subsurface Processes

Inspired mainly by observations made in Geysir (“spout”) and to a lesser extent in Strokkur (“churn”) in Iceland (Figure 1), two early conceptual models sought to explain the main features of geysers. Mackenzie (1811) proposed that eruptions are caused by the increasing pressure exerted by the expansion of steam trapped in a subsurface cavity. Bunsen (1847) suggested that eruptions are caused by ascent-driven decompression boiling in the conduit resulting from overflow. Both conceptual models have some observational support.

As discussed in Section 2, there are a variety of measurements that confirm the existence (Figure 4) and importance of subsurface cavities in the eruption process, at least at some geysers. The impulsive pressure signals generated by the nucleation and collapse of vapor bubbles induced by heating and pressure changes (e.g., Rinehart 1965 Kieffer 1984 Kedar et al. 1996, 1998 Cros et al. 2011 Vandemeulebrouck et al. 2013, 2014) allow boiling conditions to be tracked in time and space (Figure 6). Seismic energy is generated when the impulsive pressure perturbation in the liquid couples into the elastic matrix surrounding the fluid (Kedar et al. 1998, Thiéry & Mercury 2009), and these impulsive events are superposed to create a tremor-like effect (known as a hydrothermal tremor, further amplified by shallow layers that generate a site effect) when rates are high (e.g., Nicholls & Rinehart 1967 Kieffer 1984 Kedar et al. 1996, 1998 Vandemeulebrouck et al. 2014). Tilt measurements at geysering wells (Nishimura et al. 2006, Rudolph et al. 2012) and Lone Star geyser in Yellowstone (Vandemeulebrouck et al. 2014) also document the gradual recharge of shallow geyser reservoirs and conduits during the eruption cycle and abrupt drainage during eruptions (Figure 7).

The Bunsen (1847) model is supported by temperature measurements in the conduits of Old Faithful geyser, in Yellowstone (Figure 9a) Geysir, in Iceland (Figure 9b) Te Horu, in Whakarewarewa, New Zealand Velikan (“Giant”), in the Valley of Geysers, Kamchatka, Russia and geysers in El Tatio, Chile (Bunsen 1847 Rinehart 1969 Birch & Kennedy 1972 Noguchi et al. 1983 Hutchinson et al. 1997 Droznin et al. 1999 Munoz-Saez et al. 2015a,b). The temperature-depth profile at Old Faithful geyser shows that at the top of the water column in the conduit, water temperature is at the boiling temperature for pure water, and deeper in the conduit, water is slightly colder than the hydrostatic boiling temperature appropriate to the level of water in the conduit (Figure 9a). The maximum temperature in the conduit of Geysir occurs several meters below the top of the water column (Figure 9b). The differences in the shapes of the curves may reflect differences in the structure of the geysers. Whereas Old Faithful is a cone geyser, so that evaporative heat loss is low (Hurwitz et al. 2014), Geysir is a pool geyser, so that significant amounts of heat are lost to the atmosphere.

Concurrent measurements of pressure and temperature in the conduits of Old Faithful in Yellowstone (Hutchinson et al. 1997) and El Jefe in El Tatio (Munoz-Saez et al. 2015a) showed that, following an eruption, water recharge is gradual and much of the heat is added at later stages (Figure 10). Preparation of the geyser for major eruptions is accompanied, in some cases, by minor eruptions, or preplay (see Section 4.2), that may be a manifestation of fluid release from bubble traps and have the thermal consequence of heating water in the conduit. As the eruption progresses, boiling in geyser conduits propagates downward and steam generated at greater depths (possibly in cavities or bubble traps) enters the conduit, delivering latent heat to warm water in the conduit.

Convective oscillations driven by temperature inversions during the recharge period also affect accumulation of heat and steam in the conduit (Hales 1937, White 1967, Murty 1979, Kieffer 1984, Dowden et al. 1991, Hutchinson et al. 1997, Alexandrov et al. 2016), and convection may occur during all stages of an eruption cycle (O'Hara & Esawi 2013). However, in contrast to large-diameter wells, geyser conduits are typically narrow and contorted, limiting the development of convection cells and evaporative heat loss. When buoyant superheated water is convected upward, steam bubbles form and expand when the pressure decreases below the saturation pressure of the water. White (1967) suggested that convective downflow occurs generally near the sides of the conduit, but as the number of bubbles in the conduit increases with increasing temperature, the rising column expands until frictional resistance suppresses convective downflow. Enlargement of a geyser conduit (for example, after an earthquake) may result in enhanced convection and heat loss and alter the dynamics of a geyser or even lead to cessation of eruptions.

Other processes might play a role in the subsurface. The large volume change from the conversion of liquid to steam can cause large pressure changes (White 1967). A kinetic barrier to bubble nucleation has also been invoked: Steinberg et al. (1981) proposed that eruptions are driven by the nucleation of steam bubbles in a superheated fluid, and that the interval between eruptions is governed by the time it takes to achieve the required degree of superheating. There is no strong evidence in any of the reliable published data for superheating in natural geysers. However, there is anecdotal data from the late nineteenth century and early twentieth century, when it was described that dumping soap (which acts as a surfactant) into geysers led to their eruptions (Hague 1889, Torfason 1985), purportedly by removing a kinetic barrier for bubble nucleation from the superheated water. An alternative explanation is that the soap dissolved in the water and lowered the boiling temperature of the solution. Given that temperature variations throughout a geyser cycle can be as modest as a couple of degrees (e.g., Munoz-Saez et al. 2015a), a small change in boiling temperature may be sufficient to initiate eruptions.

Hydrogeological properties also influence the geysering process. Ingebritsen & Rojstaczer (1993, 1996) performed numerical simulations of multiphase fluid flow and heat transport through a porous medium, approximating the geyser system as a permeable conduit of intensely fractured rock surrounded by a less permeable rock matrix. They showed that within a narrow range of parameters that allow geyser-like behavior, eruption frequency and discharge are highly sensitive to the intrinsic permeabilities of the geyser conduit and the surrounding rock matrix, the relative permeability functions assumed for the liquid + steam mixture, and pressure gradients in the matrix. Laboratory experiments have shown that multiphase flow in rough-walled rock fractures is dominated by significant retention of the wetting phase (liquid water) and persistent instabilities, with cyclic pressure and flow rate variations (Persoff & Pruess 1995, Bertels et al. 2001).

To summarize, observations collected over the past two centuries confirm the role of subsurface geometry in accumulating and releasing fluids, highlighted by Mackenzie (1811), and the importance of the pressure dependence of the boiling temperature, highlighted by Bunsen (1847). There are additional observations, however, not explained by these two conceptual models that provide constraints on additional subsurface components of geysers: First, the volumes of the reservoir and fracture complexes from which thermal waters are discharged are significantly larger than the volumes erupted during a single eruption (Section 2). Second, chemical data (Table 1) imply that the meteoric waters in these large reservoir-fracture complexes equilibrate thermally (at ∼200°C) and chemically at depths of a few hundred meters or more before ascending to the surface where they provide the thermal energy required to drive the eruption. Third, in addition to bubble nucleation and collapse, other types of seismic signals have been recorded. Vandemeulebrouck et al. (2014) identified periodic ∼4-min ultra-long-period signals that occur during all stages of the eruption cycle and attributed these signals to ascending gas slugs. Fourth, evaporation and heat loss can have a strong effect on geyser dynamics, especially in pool geysers with a large surface area (Steinberg 1980, Weir et al. 1992, Hurwitz et al. 2014). White (1967) suggested that “the excess heat of many high-temperature systems is lost near the surface by several means, thereby explaining the absence or scarcity of geysers where they might otherwise be abundant” (p. 676), and “the large pools and vents of some geysers may lose so much heat by convection and evaporation that eruption is greatly inhibited” (p. 681). Finally, dissolved gases may influence some eruptions by lowering the boiling temperature of the solution (Hurwitz et al. 2016, Ladd & Ryan 2016).

### 4.2. Surface Eruption

The visible manifestation of geysering is the surface spout, jet, or plume that ejects a mixture of steam and liquid water. The vigor of eruptions is highly variable between geysers and during a given eruption. Eruptions range from small bubbling fountains, common in large pools, to jets that can reach heights of 115 m at Steamboat geyser in Yellowstone (Bryan 2008) and up to 450 m at Waimangu geyser in the Taupo Volcanic Zone, New Zealand, between 1900 and 1904 (Vandemeulebrouck et al. 2008). However, descriptions of jet heights are mostly anecdotal and not very accurate. Eruptions are also unsteady. Large, long-lived eruptions tend to begin as liquid dominated and evolve to steam dominated.

Many large eruptions are preceded by small preplay events that intermittently eject mostly liquid water, removing mass and pressure from the water column in the conduit. The main eruption often begins with a series of bursts before becoming approximately steady, and then the fountain height typically decreases. Pulsing with periods ranging from seconds (Kieffer 1989) to several tens of seconds (Karlstrom et al. 2013) can occur during all stages, with frequencies that glide during the course of the eruption (Karlstrom et al. 2013).

As water from the reservoir ascends through the conduit and decompresses, some of its thermal energy is converted to kinetic energy. For example, Kieffer (1989) proposed that at Old Faithful, isentropic decompression of water in the conduit initially at 116°C (measured at a depth of 21–22 m) into a 0.8-bar atmosphere loses ΔH = 3.9 kJ/kg (where H is enthalpy), which would lead to eruption velocities m/s if all the enthalpy change was converted to kinetic energy. However, if Old Faithful's reservoir temperature of 204 ± 4°C (Hurwitz et al. 2012) were considered as the initial temperature, the amount of converted energy and the jet velocity would be much greater. Measured jet velocities of several large geysers are significantly lower: ∼18 m/s in Velikan (Droznin et al. 1999) and 16–28 m/s in Lone Star geyser in Yellowstone (Karlstrom et al. 2013). This discrepancy between ballistic calculations and measured velocities suggests that drag, turbulence, and air entrainment, especially below the vent in the geyser conduit, account for much of the energy balance and significantly reduce the velocity (Karlstrom et al. 2013).

A common assumption in models for high-speed eruptions of compressible flows through vents, at both geysers and magmatic volcanoes (Bercovici & Michaut 2010), is that the speed at the vent is choked to the sound speed of the liquid + gas mixture as it passes through a constriction that acts as a nozzle. The sound speed is the velocity at which small perturbations in density or pressure propagate through the fluid (Kieffer 1977). Establishing that flow is indeed choked is a “notoriously difficult problem” (Kieffer 1989, p. 27). Karlstrom et al. (2013) found that U0 at Lone Star geyser in Yellowstone (16–28 m/s) was close to the sound speed for the estimated steam mass fraction. Munoz-Saez et al. (2015a) inferred that the sound speed inside the conduit of a small geyser at El Tatio, Chile, was similar to U0 by cross-correlating measured pressure fluctuations in the water column.

The surface manifestation of eruptions varies from bubbling pools to modest fountains to roaring jets. Eruption vigor is presumably controlled by the thermal energy available to drive the eruption, and by the geometry of the conduit through which the fluids erupt, as overpressures in the source are small (Shteinberg et al. 2013). Geysers with deep, large reservoirs lead to large quantities of thermal energy converted to kinetic energy and hence more powerful eruptions. Large water volumes permit longer eruptions. Constrictions in the conduit accelerate fluids (up to the sound speed) so that narrowing conduits favor higher eruption heights.

The heat output from geysers can be calculated from the volume of erupted water assuming isentropic decompression (Kieffer 1989, Mastin 1995, Lu & Kieffer 2009), rather than isenthalpic decompression, from a reservoir where the liquid water was stored prior to the eruption (Figure 11). The reservoir temperature can be calculated using chemical geothermometers (Fournier 1981). At Lone Star geyser in Yellowstone, with an erupted volume of 20.8 ±4.1 m 3 , a reservoir temperature of 160–170°C, and eruptions every 3 h, the calculated average heat output is 1.4–1.5 MW (Karlstrom et al. 2013).

### 4.3. Laboratory Studies

It is not possible to directly image the entire subsurface geysering process in the field, and measurements are limited to discrete locations in a complex, largely unknown plumbing system. Laboratory models thus provide an opportunity to image and measure the geysering process directly and in a controlled manner—parameters can be varied systematically, the plumbing geometry can be simplified, and variables such as pressure and temperature can be measured.

Laboratory studies have been used to show that steady heating and recharge can lead to episodic eruptions (Munby 1902, Forrester & Thune 1942, Steinberg et al. 1982), to show how increasing complexity of plumbing geometries results in greater variation in discharge styles and eruption intervals (Namiki et al. 2016), to understand the effects of geometry on convection and hence temperature in the conduit (Sherzer 1933), to show how increasing reservoir temperature increases the vigor of eruptions (Toramaru & Maeda 2013), to show how the decrease in reservoir pressure over the course of the eruption leads to recharge and the end of eruption (Lasic 2006), to show how bubble formation and collapse generates weak high-frequency tremors (Anderson et al. 1978), and to show how intermittent modulation of the rate of boiling and the closely coupled accelerations and decelerations of the water column generate strong low-frequency tremors (Anderson et al. 1978).

Laboratory studies document how boiling conditions in the reservoir propagate into the conduit as expulsion of water at the surface decompresses the remaining water (Anderson et al. 1978, Lasic 2006). They also provide a tool to understand irregularity in eruptions. For example, Steinberg (1999) showed that the duration of eruption controls the duration of the following quiescent period, and that it is the eruption duration that is stochastic.

Laboratory studies with bubble traps confirm the inferences from natural geysers that vapor can accumulate and then be released episodically, leading to both minor (preplay) and major eruptions (e.g., Davis 2012). Vapor discharged during minor eruptions progressively warms the shallower parts of the geyser, such as the conduit, so that boiling conditions can eventually be reached everywhere in the conduit, leading to larger and more sustained eruptions (Adelstein et al. 2014). This is consistent with the gradual increase in intensity of regularly spaced minor eruptions leading up to the major eruption at some natural geysers (Namiki et al. 2014).

In general, even modest complexity in laboratory models (as in numerical models), such as a single bend in the conduit (Davis 2012, Adelstein et al. 2014) or multiple reservoirs supplying water to the conduit (Anderson et al. 1978, Cross 2010), can lead to irregular eruption intervals. The regularity of many natural geysers is thus all the more remarkable.

## Contents

The existence of escape velocity is a consequence of conservation of energy and an energy field of finite depth. For an object with a given total energy, which is moving subject to conservative forces (such as a static gravity field) it is only possible for the object to reach combinations of locations and speeds which have that total energy and places which have a higher potential energy than this cannot be reached at all. By adding speed (kinetic energy) to the object it expands the possible locations that can be reached, until, with enough energy, they become infinite.

For a given gravitational potential energy at a given position, the escape velocity is the minimum speed an object without propulsion needs to be able to "escape" from the gravity (i.e. so that gravity will never manage to pull it back). Escape velocity is actually a speed (not a velocity) because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field (provided its path does not intersect the planet).

An elegant way to derive the formula for escape velocity is to use the principle of conservation of energy (for another way, based on work, see below). For the sake of simplicity, unless stated otherwise, we assume that an object will escape the gravitational field of a uniform spherical planet by moving away from it and that the only significant force acting on the moving object is the planet's gravity. Imagine that a spaceship of mass m is initially at a distance r from the center of mass of the planet, whose mass is M, and its initial speed is equal to its escape velocity, v e > . At its final state, it will be an infinite distance away from the planet, and its speed will be negligibly small. Kinetic energy K and gravitational potential energy Ug are the only types of energy that we will deal with (we will ignore the drag of the atmosphere), so by the conservation of energy,

We can set Kƒinal = 0 because final velocity is arbitrarily small, and Ugƒinal = 0 because final distance is infinity, so

The same result is obtained by a relativistic calculation, in which case the variable r represents the radial coordinate or reduced circumference of the Schwarzschild metric. [6] [7]

Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity and end at infinity with a residual speed of zero, without any additional acceleration. [8] All speeds and velocities are measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point.

In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s). However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s. Note that this escape velocity is relative to a non-rotating frame of reference, not relative to the moving surface of the planet or moon (see below).

The escape velocity is independent of the mass of the escaping object. It does not matter if the mass is 1 kg or 1,000 kg what differs is the amount of energy required. For an object of mass m the energy required to escape the Earth's gravitational field is GMm / r, a function of the object's mass (where r is the radius of the Earth, G is the gravitational constant, and M is the mass of the Earth, M = 5.9736 × 10 24 kg ). A related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass. An object has reached escape velocity when the specific orbital energy is greater than or equal to zero.

### From the surface of a body Edit

where r is the distance between the center of the body and the point at which escape velocity is being calculated and g is the gravitational acceleration at that distance (i.e., the surface gravity). [9]

Note that this escape velocity is relative to a non-rotating frame of reference, not relative to the moving surface of the planet or moon, as we now explain.

### From a rotating body Edit

The escape velocity relative to the surface of a rotating body depends on direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s at the equator, a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s relative to the moving surface at the point of launch to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s relative to that moving surface. The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral (latitude 28°28′ N) and the French Guiana Space Centre (latitude 5°14′ N).

### Practical considerations Edit

In most situations it is impractical to achieve escape velocity almost instantly, because of the acceleration implied, and also because if there is an atmosphere, the hypersonic speeds involved (on Earth a speed of 11.2 km/s, or 40,320 km/h) would cause most objects to burn up due to aerodynamic heating or be torn apart by atmospheric drag. For an actual escape orbit, a spacecraft will accelerate steadily out of the atmosphere until it reaches the escape velocity appropriate for its altitude (which will be less than on the surface). In many cases, the spacecraft may be first placed in a parking orbit (e.g. a low Earth orbit at 160–2,000 km) and then accelerated to the escape velocity at that altitude, which will be slightly lower (about 11.0 km/s at a low Earth orbit of 200 km). The required additional change in speed, however, is far less because the spacecraft already has a significant orbital speed (in low Earth orbit speed is approximately 7.8 km/s, or 28,080 km/h).

### From an orbiting body Edit

The escape velocity at a given height is 2 >> times the speed in a circular orbit at the same height, (compare this with the velocity equation in circular orbit). This corresponds to the fact that the potential energy with respect to infinity of an object in such an orbit is minus two times its kinetic energy, while to escape the sum of potential and kinetic energy needs to be at least zero. The velocity corresponding to the circular orbit is sometimes called the first cosmic velocity, whereas in this context the escape velocity is referred to as the second cosmic velocity. [10]

For a body in an elliptical orbit wishing to accelerate to an escape orbit the required speed will vary, and will be greatest at periapsis when the body is closest to the central body. However, the orbital speed of the body will also be at its highest at this point, and the change in velocity required will be at its lowest, as explained by the Oberth effect.

### Barycentric escape velocity Edit

Technically escape velocity can either be measured as a relative to the other, central body or relative to center of mass or barycenter of the system of bodies. Thus for systems of two bodies, the term escape velocity can be ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. In gravitational fields, escape velocity refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field. In most situations involving spacecraft the difference is negligible. For a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is 253.5 am/s (8 nanometers per year) faster than the escape velocity relative to the mutual center of mass. [ citation needed ]

### Height of lower-velocity trajectories Edit

which, solving for h results in

Unlike escape velocity, the direction (vertically up) is important to achieve maximum height.

If an object attains exactly escape velocity, but is not directed straight away from the planet, then it will follow a curved path or trajectory. Although this trajectory does not form a closed shape, it can be referred to as an orbit. Assuming that gravity is the only significant force in the system, this object's speed at any point in the trajectory will be equal to the escape velocity at that point due to the conservation of energy, its total energy must always be 0, which implies that it always has escape velocity see the derivation above. The shape of the trajectory will be a parabola whose focus is located at the center of mass of the planet. An actual escape requires a course with a trajectory that does not intersect with the planet, or its atmosphere, since this would cause the object to crash. When moving away from the source, this path is called an escape orbit. Escape orbits are known as C3 = 0 orbits. C3 is the characteristic energy, = −GM/2a, where a is the semi-major axis, which is infinite for parabolic trajectories.

If the body has a velocity greater than escape velocity then its path will form a hyperbolic trajectory and it will have an excess hyperbolic velocity, equivalent to the extra energy the body has. A relatively small extra delta-v above that needed to accelerate to the escape speed can result in a relatively large speed at infinity. Some orbital manoeuvres make use of this fact. For example, at a place where escape speed is 11.2 km/s, the addition of 0.4 km/s yields a hyperbolic excess speed of 3.02 km/s:

If a body in circular orbit (or at the periapsis of an elliptical orbit) accelerates along its direction of travel to escape velocity, the point of acceleration will form the periapsis of the escape trajectory. The eventual direction of travel will be at 90 degrees to the direction at the point of acceleration. If the body accelerates to beyond escape velocity the eventual direction of travel will be at a smaller angle, and indicated by one of the asymptotes of the hyperbolic trajectory it is now taking. This means the timing of the acceleration is critical if the intention is to escape in a particular direction.

If the speed at periapsis is v , then the eccentricity of the trajectory is given by:

This is valid for elliptical, parabolic, and hyperbolic trajectories. If the trajectory is hyperbolic or parabolic, it will asymptotically approach an angle θ from the direction at periapsis, with

The speed will asymptotically approach

In this table, the left-hand half gives the escape velocity from the visible surface (which may be gaseous as with Jupiter for example), relative to the centre of the planet or moon (that is, not relative to its moving surface). In the right-hand half, Ve refers to the speed relative to the central body (for example the sun), whereas Vte is the speed (at the visible surface of the smaller body) relative to the smaller body (planet or moon).

The last two columns will depend precisely where in orbit escape velocity is reached, as the orbits are not exactly circular (particularly Mercury and Pluto).

Let G be the gravitational constant and let M be the mass of the earth (or other gravitating body) and m be the mass of the escaping body or projectile. At a distance r from the centre of gravitation the body feels an attractive force

The work needed to move the body over a small distance dr against this force is therefore given by

The total work needed to move the body from the surface r0 of the gravitating body to infinity is then [15]

In order to do this work to reach infinity, the body's minimal kinetic energy at departure must match this work, so the escape velocity v0 satisfies

Category: satellites of planets

Ice moon of Saturn shows its full splendor. In the foreground, the bright white of Enceladus detaches immense shadows of Saturn's rings as seen in the background.
This photo was taken on 28 June 2007, at a distance of approximately 291 000 km, by the Cassini spacecraft, using its camera angle during its mission 'Equinox'.
This perfectly round white side of Enceladus, measuring 504 km in diameter.
The objective of the Cassini spacecraft is on 15 October 1997, the date of its introduction, the study of the planet Saturn and several of its satellites, including Titan. The space probe Cassini-Huygens, consisting of the orbiter Cassini and Huygens module is in orbit around the planet and is about to complete his mission 11 years.

Huygens, which aimed to land on the moon Titan, was raised on Titan on 14 January 2005 returning to Earth, remote 1.2 billion km, information and spectacular images.

## Organic Materials Erupt from Geysers on Enceladus

O rbiting Saturn, the icy moon Enceladus is home to numerous active geysers, which regularly erupt with plumes of water and rocky material. While some of the water released from these vents falls across the surface of that world as snow and ice, a portion soars into space. A new study shows organic compounds, essential to the formation of amino acids, are mixed in with the material erupting from these vents.

Given energy and a favorable climate, these organic compounds could form amino acids. The energy required to form these molecules on Earth is supplied by hydrothermal vents on the ocean floor. Researchers speculate the geysers that feed the vents on Enceladus might provide the energy needed to drive the formation of amino acids on Enceladus.

“If the conditions are right, these molecules coming from the deep ocean of Enceladus could be on the same reaction pathway as we see here on Earth. We don’t yet know if amino acids are needed for life beyond Earth, but finding the molecules that form amino acids is an important piece of the puzzle,” said Nozair Khawaja, of the Free University of Berlin.

The materials detected in data from the Cassini spacecraft are composed of nitrogen- and oxygen-bearing compounds, condensed into ice grains. The Cosmic Dust Analyzer, or CDA, which detected ice grains emitted from Enceladus into Saturn’s E ring, collected the data used in this study.

“Saturn’s moon Enceladus is erupting a plume of gas and ice grains from its south pole. Linked directly to the moon’s subsurface global ocean, plume material travels through cracks in the icy crust and is ejected into space. The subsurface ocean is believed to be in contact with the rocky core, with ongoing hydrothermal activity present,” researchers detailed in the Monthly Notices of the Royal Astronomical Society.

In February and March , Cassini flew within 500 kilometers (310 miles) of the surface of Enceladus. By comparison, Voyager 1 never came closer than 90,000 km (nearly 56,000 miles) from the surface of Enceladus during its 1981 flyby.

The Moon, a Ring, how Romantic!

Enceladus is a moderately-sized moon, measuring just 500 km (310 miles) across, about as wide as the state of Arizona.

It is one of the few moons in the Solar System known to have an atmosphere (although it is exceedingly thin). Its mass, 680 times smaller than our own Moon, means Enceladus is unable to hold onto a thick atmosphere, allowing water vapor to escape to space.

This tenuous atmosphere was detected through small changes in the magnetic field of Saturn caused by electrically-charged material surrounding Enceladus.

In 2005, seeing signs of water in the thin atmosphere of that moon provided the first evidence water is continually replenished by geysers on that world.

As the moon rotates (roughly) once every 33 hours, a continuous rain of snow and ice falls, making Enceladus the brightest object in the Solar System. This world is thought to house a vast ocean of salty water beneath its frozen crust.

There, organics are thought to mix with water, before rising up where they freeze into grains of ice hidden in fractures within fractures in the crust of the moon. Rising plumes of water and subsurface material rides up from below, carrying the material to the surface in the form of an eruption, researchers theorize.

Cassini also found that one of the major rings of Saturn — the E ring — is continuously refreshed with new material from the geysers of Enceladus.

“The material shoots out at about 800 miles per hour (400 meters per second) and forms a plume that extends hundreds of miles into space. Some of the material falls back onto Enceladus, and some escapes to form Saturn’s vast E ring,” NASA explains.

This ring, discovered in 1966, is not as defined, or flat, as the other rings of Saturn. This formation resembles a giant doughnut surrounding Saturn.

“Well, heaven forgive him! and forgive us all! Some rise by sin, and some by virtue fall:
Some run from brakes of ice, and answer none: And some condemned for a fault alone.”
― William Shakespeare, Measure for Measure

The Cassini Mission ended in September 2017, as the vehicle was purposely commanded to undertake a death dive into the dense atmosphere of Saturn. This act was undertaken as Cassini faded, preventing the spacecraft from colliding with any of Saturn’s dozens of moon in the future.

In Greek mythology, Enceladus was a giant who fought a legendary battle against Athena during the Gigantomachy, a mythical war between the gods and giants. This story provided a popular theme for vases, plates, and works of art.

Out in the solar system, several worlds are potential homes for simple life, like that which dominated our own world for the majority of its history. This new finding, combined with the possibility of a layer of complex organic materials at the surface of ocean of Enceladus, makes this world a promising target in the quest for extraterrestrial life.

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