Mathematical modelling contributes to NASA space mission and inspires public interest in science
Submitting Institution
University of LeicesterUnit of Assessment
Mathematical SciencesSummary Impact Type
TechnologicalResearch Subject Area(s)
Earth Sciences: Geology, Oceanography
Engineering: Interdisciplinary Engineering
Summary of the impact
NASA's Cassini mission to Saturn's icy moon Enceladus in 2009-10
investigated the presence of explosive ice geysers towering over the south
pole of the planet. The geysers consist of vapour and ice particles which
rise up to 1,000 kilometres above Enceladus' surface. The source of these
jets has been hotly contested. Cassini's mission was to fly as close as
possible to the plumes to search for evidence of sub-surface water
containing the building blocks of life.
Mathematical modelling, conducted at Leicester, allowed the mission
designers to calculate the possibility of the Cassini Spacecraft colliding
with dust from the Enceladus jets, with potentially catastrophic results,
enabling the craft to be manoeuvred as close as safely possible to the
moon's surface to capture the images it required.
The mission, with an estimated $3.26 billion cost, was successful —
gathering evidence that the research team's hypothesis of a subterranean
sea on Enceladus was correct — a revelation which has inspired public
interest around the world.
Underpinning research
In 2008, Nikolay Brilliantov (University of Leicester since 2007, now
Chair, Professor in Applied Mathematics) collaborated with Jurgen Schmidt
and Frank Spahn (both Institute of Physics, University of Potsdam,
Germany) publishing research in Planetary and Space Science [1]. The
research analysed previously published qualitative models of the geysers
of Enceladus and examined two hypotheses for the underlying cause of
Enceladus' geysers already proposed by astronomers, in the light of data
gathered by Cassini.
The first `Cold Faithful hypothesis' assumes an explosive boiling
of subsurface liquid water, when pressure exerted by the ice crust is
suddenly released due to an opening crack. In the second hypothesis, `Frigid
Faithful', the existence of a deep shell of clathrates below
Enceladus' south pole is conjectured; clathrates can decompose explosively
when exposed to vacuum through a fracture in the outer icy shell.
Development of a new hypothesis
Brilliantov elaborated mathematical models that quantified both
hypotheses and his collaborators performed the numerical computations. It
was found that, for the Cold Faithful model, the explosive boiling can't
provide the velocities of icy particles observed in the plume. It also
found that the low temperatures of the Frigid Faithful model implied a too
dilute vapour to support the observed high particle fluxes in Enceladus'
plume.
In the same year, the same team published a novel hypothesis [2],
underpinned by the new mathematical model by Brilliantov, to explain the
icy geysers. The explanation was a liquid water ocean with a large vapour
reservoir below Enceladus' south pole. Smaller velocities for the geyser's
grains than for the vapour had been difficult to understand. The gas and
dust were too dilute in the plume to interact, so the difference had to
arise below the surface. The team published a model for grain condensation
and growth in channels of variable width showing that repeated wall
collisions of grains, with re-acceleration by the gas, induced an
effective friction, offering a natural explanation for the reduced grain
velocity. The gas seemed to form near the triple point of water; gas
densities corresponding to sublimation from ice are generally too low to
support the measured particle fluxes. This in turn suggested liquid water
ocean below Enceladus' south pole. This theory was in a quantitative
agreement with data gathered so far by Cassini.
In 2009, Brilliantov elaborated a theory quantifying the sodium content
in the icy geysers. He provided the mathematical modelling expertise , in
a the team comprising colleagues from Potsdam, Heidelberg, Gottingen and
Leicester, providing strong evidence [3] that supported the theory that
liquid water, rather than frozen water, below Enceladus' south pole was
responsible for the icy geysers. After studying data from the Cosmic Dust
Analyzer (CDA) on board the Cassini spacecraft and combining this data
with laboratory experiments, the team reported the detection of sodium
salts among the dust ejected in the Enceladus plume, hinting at the salty
ocean deep below and thus confirming their theory. The results of the
study imply that the concentration of sodium chloride in the ocean can be
as high as that of Earth's oceans.
Brilliantov's mathematical model was combined with computational
modelling of the grain sizes and laboratory experiments performed by the
rest of the team. This explained the observed concentration of salt in icy
grains, especially, for the part of grains with a low salt concentration.
Their conclusion through analysis of the distribution of grain size, was
that the type and speed of particles could only have been produced from
liquid water, hence the hypothesis of the existence of a subterranean
ocean and the conclusion that the grain sizes and speed were unlikely to
damage Cassini.
This work enabled NASA to conclude that the risks were such that it
deemed `safe' for the mission to fly closer to the moon's surface and thus
undertake the exploration leading to the subsequent important discoveries.
References to the research
1. N. Brilliantov, J.Schmidt and F. Spahn, Geysers of Enceladus:
Quantitative analysis of Qualitative models, Planetary and Space Science,
56 (2008), pp. 1596-1606.
2. J. Schmidt, N. Brilliantov, F. Spahn, and S. Kempf, Slow dust in
Enceladus' plume from condensation and wall collisions in tiger stripe
fractures, Nature, 451 (2008), pp. 685-688.
3. F. Postberg, S. Kempf, J. Schmidt, N. Brilliantov, A. Beinsen, B.
Abel, U. Buck & R. Srama, Sodium salts in E-ring ice grains from an
ocean below the surface of Enceladus, Nature, 459 (2009) pp. 1098 - 1101
Details of the impact
The Cassini Missions
Cassini-Huygens is a flagship-class NASA-ESA-ASI robotic spacecraft sent
to the Saturn system. It has studied the planet and its many natural
satellites since arriving there in 2004, also observing Jupiter, the
Heliosphere, and testing the theory of relativity. Sixteen European
countries and the United States make up the team responsible for
designing, building, flying and collecting data from the Cassini orbiter
and its Huygens probe. Cassini completed its initial four-year mission to
explore the Saturn System in June 2008 and the first extended mission,
called the Cassini Equinox Mission, in September 2010.
Cassini's discovery of an icy plume shooting from one of Saturn's moons,
and subsequent observations of the spray containing complex organic
chemicals have caused much debate and conjecture on the part of
astronomers. Brilliantov's work has helped to identify warm, liquid water
ocean encased beneath the surface of Enceladus' moon as being the most
likely cause of the icy geysers.
Evaluation of flightpath
Brilliantov's work was used by NASA in the planning of the Cassini
mission in 2009-2010 in an absolutely fundamental way. The contribution is
summarised in a statement by one of the Principal Investigators of the
Cassini Mission, Prof. L. Esposito, who wrote that:
"... the model of Schmidt et al 2008 (J. Schmidt, N. Brilliantov, F.
Spahn, and S. Kempf, Nature, 451 (2008) 685) has been used to evaluate
the planned flybys of the spacecraft of the Cassini mission in
2009-2010, allowing the mission designers to calculate the danger of the
Cassini Spacecraft colliding with dust in the Enceladus plumes and jets.
This has allowed NASA's Cassini Project to reduce the hazardous impacts
of the probe with the ice grains within the Enceladus plume."
Economic impact
The total cost of the mission was about $3.26 billion, which was
paid for by the US, the European and the Italian Space Agencies. Had the
Cassini spacecraft collided with the plumes due to failure to take account
of the research underpinning this impact case, this significant investment
would have been largely lost.
Cultural impact
The team's research enabled the Cassini mission to carry out a very close
sweep of the moon and capture unique data that provided further evidence
of the presence of a subterranean sea and verification of the chemical
composition of the moon's atmosphere.
The significance of the presence of the liquid water sea has implications
for mankind. Tidal heating is keeping Enceladus warm and hotspots
associated with the fountains have been pinpointed. With heat, organic
chemicals and, potentially liquid water, Enceladus could be a place where
primitive life forms might evolve. Questions surrounding Enceladus'
"astrobiological potential" are at the heart of many investigations being
conducted in the Solstice Mission. Because of its large astrobiological
potential a forthcoming European mission "Enceladus Explorer" is
planned including a base station on the Enceladus surface and ice drilling
to examine the liquid ocean for any traces of microorganisms.
The mission has inspired extensive media and public interest on a global
scale. The discovery of the underground ocean and potential life in outer
space has, understandably, been the source of widespread media coverage
reaching millions of people (e.g. New York Times articles reaching almost
2 million readers plus online hits).
Social media statistics also illustrate how inspiring this story is to
the general population. As of June 2013 #Enceladus had almost 35,000
mentions (76% of which were retweets showing that the stories have gone
viral) and Life on Saturn is searched for by 5,400 people a month on
Google.
NASA has a comprehensive outreach programme and has disseminated the
findings of the Cassini mission to millions of people including well used
teaching materials in schools. One of the top documentary films of 2010 "7
Wonders of the Solar System "annotates" The seven wonder of our
solar system are discussed: Enceladus' geysers, Rings of Saturn,
Jupiter's Great Red Spot, the Asteroid Belt, Mars' Olympus Mons, the
Surface of the Sun, and planet Earth"; it has been watched by
several hundred thousand people.
Sources to corroborate the impact
- Factual statement from the Principal Investigator of the Cassini
Ultraviolet Imaging Spectrograph (LASP, Boulder, USA).
- Article from the New York Times, "Saturn Imitates Louis XIV", February
28, 2008:
http://tierneylab.blogs.nytimes.com/2008/02/28/saturn-imitates-louis-xiv/
- Report from the BBC on the underground sea on Enceladus on 25 June
2009:
http://news.bbc.co.uk/1/hi/sci/tech/8115148.stm
- Statement from the Co-Investigator of the Cosmic Dust Analyser on the
Cassini Spacecraft.
- Article in Sciencedaily http://www.sciencedaily.com/releases/2008/02/080222112324.htm
- Article in Physorg http://www.physorg.com/news122898790.html
- Report by The Cheers News Agency
http://newsagency.thecheers.org/Science/news_12848_Scientists-unravel-secret-behind-Saturns-moons-mysterious-plumes-of-dust-and-water-vapour.html
- Report in Thaindian News http://www.thaindian.com/newsportal/health/scientists-unravel-secret-behind-saturns-moons-mysterious-plumes-of-dust-and-water-vapour-2_10020607.html
- JPL News Feature http://saturn.jpl.nasa.gov/news/cassinifeatures/
- On Space.Com http://www.space.com/4935-mystery-saturn-watery-moon-solved.html
- NASA report http://www.nasa.gov/mission_pages/cassini/whycassini/cassinif-20080207.html