Phobos is the larger moon of Mars. The crater on the near end is 10 kilometers in diameter.
1) How fast do Mars' moons move? The two moons of Mars, Phobos and Deimos, were discovered in 1877 by Asaph Hall. He measured how far they were from Mars, and so learned how large their orbits are. By watching the moons as they moved, he also measured how long each took to orbit Mars (the orbital period). Because they are close to Mars, they move very fast.
How fast do Phobos, Deimos, and our own Moon move? To calculate their speeds, remember that speed = distance/time, and that the distance around a circle is
2 pi x radius (pi=3.14).
Moon Radius of Orbit (km) Orbit Period (Earth days) Orbit Period (seconds) Phobos 9,380 0.32 27,500 Deimos 23,500 1.26 109,000 Moon 384,400 27.32 2,350,000 2) How much does Mars weigh? Back in the 1600's, Isaac Newton proved that the speed of a moon was related to the mass of its planet and its distance from the planet:
M = R V 2 / G
where M is the mass of the planet (kilograms), V is the moon's speed (kilometers per second), and R is the radius of the moon's orbit (kilometers). G is the universal gravitational constant, 6.67 x 10-20 km3 kg-1 sec-2 . So, with the speeds calculated in part 1, what is Mars' mass? How massive is Mars compared to Earth?
3) Phobos in the sky with Deimos. Both Mars and the Earth rotate so that the Sun rises in the east and sets in the west, and their moons all orbit in the same direction as the planets rotate. Earth's Moon has a very long orbital period compared to the length of an Earth day, so on a given day our Moon moves east to west across the sky with minor movement relative to the Sun or stars. However, this is not the case for Mars' moons. By comparing their orbital periods with the length of a martian day (1.026 Earth days), determine how the martian moons will appear to move across the sky to an observer on the surface of Mars. (Hint: Sketch how the orbits of Mars and its moons look to an observer looking down at Mars from very far above Mars' north pole. From this view, Mars rotates counterclockwise, and its moons orbit counterclockwise.) In one Mars day, Mars rotates on its axis once. In that Mars day, how many times do Phobos and Deimos go around Mars?
4) The shadow of Phobos. You are standing on the equator of Mars at noon and Phobos, about 21 km in diameter, passes directly overhead. How long will you be in the shadow of Phobos? To figure this out, compare the velocity of Phobos in orbit to your velocity on the equator of Mars, 0.2405 kilometers per second, and calculate the velocity of Phobos relative to you. The time you will be in the shadow is simply the length of Phobos' shadow divided by its velocity relative to you.
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© Lunar and Planetary Institute (1997)
