Photojournal.jpl.nasa/catalog/PIA02031

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 Earth’s oceans. History 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. 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 Earth’s. 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-BPSPP-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 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. 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. 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/history.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