Photojournal.jpl.nasa.govcatalogPIA02031

1
Martian Tides
Jais Brohinsky Claudia Meza

Abstract Question Were there water on Mars, how
would the tides compare to those on Earth? We
were able to calculate, in Newtons, the tidal
forces of Mars moons and the sun on a 14 million
km3 Martian ocean. These results were compared
to those of the moon and the sun on Earths
oceans.

History Connections between the tides, the moon
and sun were made as early as 2000BC but there
isnt surviving evidence of reliable predictions
or even a theory behind the phenomena. It wasnt
until Isaac Newton was able to apply his
formulation of his laws of gravitational
attraction that more applied research began as
well as construction of machines that could give
more exact predictions. Lord Kevin designed the
first of these hand cranked tidal predicting
machines in 1873, using the principle of harmonic
analysis. Pulleys, cogs and strings were set in
angles which corresponded to the harmonic
constants. A number of shafts corresponded to the
different frequency components of the tide
raising effect. A system of pulley blocks and
ropes were arranged to add up the effect from the
many shafts and to produce the tidal curve. The
wave predictions were drawn out on a scroll of
paper rotated by the machinery.
Tidal Force Results Mars Phobos 1.6307E11
N Earth Moon 3E15 N Mars Deimos 2.3588E9
N Mars Sun Earth Sun Aphelion
1.6311E12 N Aphelion 1.28E15 N
Perihelion 2.8615E12 N Perihelion 1.4E15
N Semi-major 2.1326E12 N Semi-major
1.36E15 N

• Hypotheses
• The moon and the sun are responsible for the
  tides on Earth, yet the sun is so far away that
  it's gravitational pull is almost nothing
  compared to that of the moon. Mars has two moons,
  therefore the pulls of gravity will vary with
  their orbits. The result will be very irregular
  tides as the gravitational pulls interact as the
  moons orbit.  
• There are no tides on Mars.
• The tides will be much stronger on Mars because
  there are two moons where as Earth only has one.
• The tidal effects on Mars will be much less than
  that on Earth because the moons are made almost
  completely of carbon and therefore are much less
  massive than ours
• There will be multiple high tides a day, but
  never constant because one moon has a period of
  30 hours and the other has a period of 8 hours.

Method We decided to compare the hypothetical
tides of Mars and those of the Earths by only
focusing on the extreme spring tides of each
planet. The highest tides experiences on Earth
are 50 feet or 600 inches in the Bay of Fundi.
The most extreme Martian high tide according to
our tidal force results is 1/1000 of the
Earths. 600 x .001 0.6 inches Taking into
account Martian gravity compared to that on
Earth, we were able to find the highest tide on
Mars. 0.6/0.38 1.579 inches
Mars Earth Diameter 6794 km 12,756
km Mass 6.42E23 kg 5.97E24 kg Orbital
Period 779.94 days 365.256 days Tilt of
Axis 25.19o 23.45o Surface Gravity
0.38 1.0

(Compared to Earth)

Aphelion 2.49E8
km 1.53E8 km Perihelion 2.07E8 km
www.nwrc.usgs.gov/world/images/mars.jpg
1.48E8 km www.scienceexperts.com/Earth-NASA-BP
SPP-Ed4.jpg Semi-major Axis 2.28E8 km
1.49E8
km Phobos Deimos Diameter 28x23x20
km 16x12x10 km Mass 1.06E16 kg 2.4E15
kg Orbital Period 7.85 hours 31.09
hours Average Distance 9378 km
23,460 km

www.unet.univie.ac.at/a9503672/astro/pics.html
www.gw.marketingden.com
/planets/mars.html
The Martian Ocean In the early 1980s,
scientists began to look toward Earth to explain
the Martian terrain. Tim Parker was surveying
land in the southwest, measuring the ancient
shorelines of North Americas once largest lake
Lake Bonneville (now Utahs Great Salt Lake). In
1984, Parker looked at the Viking photographs of
Cydonia Mensae, the tablelands on the edge of
Arabia Terra. Parker found traces of what he had
seen studying Lake Bonneville wave erosion
around elevated islands and fossilized sand bars.
He followed the shorelines north and east along
the edge of Arabia Terra and into Deuteronilus
Mensae. As Parker continued to follow, he
realized that the traces he found were not the
shorelines to a giant lake, but something much
vaster, something like an ocean.
Parker came up with two major lines that seemed
to hold around the globe. They were Contact 1
and Contact 2. When further investigated, (in
2001 using the Mars Global Surveyors altimeter,
MOLA) it was discovered that the altitude of
Contact 1 was so irregular that it could not be a
shoreline. Contact 2, however, proved stable.
Around the planet, Contact 2s elevation changed
by less than a thousand meters. Even more
convincing was how it followed the terrain,
rising and falling with the elevation. Further
testing revealed that areas north of Contact 2
were smooth, fitting the idea of an ocean whose
sedimentation makes sea floors smooth. When the
ocean created by Contact 2 was measured, it was
estimated to contain 14 million cubic kilometers.
Though 14 million cubic meters is enough water to
cover the Martian surface with a depth of about
one hundred meters, it is only one percent of
amount of water in our oceans here on Earth.
Conclusions From our calculations we see that
the tides on Mars are about 1/1000 of those on
Earth. Since the highest tides on Earth are
about 50 feet, the most extreme Martian high tide
would deform an ocean by about an inch and a
half. Here on Earth, the moon exerts a greater
tidal force than the sun. On Mars, Phobos force
is 10,000 times less than that of our moon on
Earth. Deimos tidal force is 100 times less
than Phobos, and 1,000,000 times less than our
moon. Surprisingly, Mars tides would be
affected more by the sun than by either moon.
This coincides with our hypothesis that the tidal
effects on Mars will be much less than that on
Earth because the moons are made almost
completely of carbon and therefore are much less
massive than ours. The gravitational pull will be
minimal.
Phobos and Deimos Mars two moons, Phobos (fear)
and Deimos (panic), were named for the horses
that pulled the Greek war god Ares chariot. The
two moons are thought to be captured asteroids
from the nearby outer asteroid belt. Deimos, the
smallest moon in our known solar system, is
considered the most recent addition. The moons
are composed of mainly carbon and ice making it a
possibility that they are both C-type asteroids.
Typical of carbon-rich asteroids, Phobos and
Deimos have low densities, 1900 kg/m3 and 1760
kg/m3 respectively and reflect less than 10 of
sunlight. Today, Phobos mean distance from
Mars is 9377 km and it orbits with a period of
0.3189 Martian days or just under eight hours.
Since Mars rotation is slower than the orbital
period of Phobos, the moon moves behind Mars
tidal bulge, holding it back. Because the tidal
bulge is behind a line connecting the centers of
Mars and Phobos, the moon is actually being
slowed and pulled toward the equator. In about
50 million years, Phobos will either break apart
due to the tidal forces or crash into Mars.
Deimos, with a mean distance of 23,436 km and an
orbital period of 1.2624 Martian days or about 31
hours, orbits slower than Mars rotation and is
therefore moving away from the planet.
Deuteronilus Mensae
Cydonia Mensae

• References
• Barrow-Green, June. Poincare and the Three Body
  Problem. USA the American Mathematical Society,
  1997.
• Bartlett, James. Classical and Modern Mechanics.
  Alabama University of Alabama Press, 1975
• Baumann, Gerd. Mathematica in Theoretical
  Physics. New York TELOS, 1996
• Freedman, Roger and Kaufmann, William. Universe
  6th edition. USA W.H. Freeman and Company, 2002
• Moore, Thomas. Six ideas that shaped physics. New
  York McGraw-Hill, 2003
• Morton, Oliver. Mapping Mars. New York Picador,
  2002
• www.nasa.gov 
• www.soes.soton.ac.uk/research/groups/soton_water/h
  istory.html

Formulas
Photojournal.jpl.nasa.gov/catalog/PIA02031
F(tidal) 2GM1M2d r3
G Gravitational Constant (6.67 x 10-11) M1
Mass of moon or sun M2 Mass of Mars r
Distance between Mars and moon or sun a Martian
radius d Diameter of Mars