Martian Tides
Jais Brohinsky & Claudia Meza
Abstract
History
Tidal Force Results
Question: Were there water on Mars, how would the tides compare to
those on Earth?
Connections between the tides, the moon and sun were made as early as 2000BC but
there isn’t surviving evidence of reliable predictions or even a theory behind the
phenomena. It wasn’t 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.
Mars – Phobos 1.6307E11 N
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 Earth’s oceans.
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.
Earth – Moon 3E15 N
Mars – Deimos 2.3588E9 N
Mars – Sun
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.
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
Method
• 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.
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
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 Earth’s.
Surface Gravity
0.38
(Compared to Earth)
1.0
The Martian Ocean
Aphelion
2.49E8 km
1.53E8 km
In the early 1980’s, 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 America’s once largest lake: Lake Bonneville (now Utah’s 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.
Perihelion
2.07E8 km
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.nwrc.usgs.gov/world/images/mars.jpg
www.unet.univie.ac.at/a9503672/astro/pics.html
1.48E8 km
600 x .001 = 0.6 inches
www.scienceexperts.com/Earth-NASA-BPSPP-Ed4.jpg
0.6/0.38 = 1.579 inches
Conclusions
www.gw.marketingden.com/planets/mars.html
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.
Cydonia
Mensae
Deuteronilus
Mensae
Photojournal.jpl.nasa.gov/catalog/PIA02031
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 Surveyor’s 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 2’s 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.
Taking into account Martian gravity
compared to that on Earth, we were able
to find the highest tide on Mars.
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.
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.
References
•Barrow-Green, June. Poincare and the Three Body Problem.
USA: the American Mathematical Society, 1997.
Formulas
•Bartlett, James. Classical and Modern Mechanics. Alabama:
University of Alabama Press, 1975
F(tidal) = 2GM1M2d
•Baumann, Gerd. Mathematica in Theoretical Physics. New York:
TELOS, 1996
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
•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/history.html