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The mass and average density of Mars, if the diameter of Mars is
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Answer to Problem 6Q
Solution:
Explanation of Solution
Given data:
The diameter of Mars is
Phobos’ orbital period is
The altitude of Phobos is
Formula used:
The expression for Kepler’s Third Law, for the orbital period of a planet or a satellite, is given as:
Here,
Write the expression for radius.
Here,
Write the formula for the volume of a sphere.
Here,
Write the expression for density
Here,
Explanation:
Phobos’ orbital radius is:
Recall the expression for Kepler’s Third Law for the orbital period of a satellite:
Rearrange the expression in terms of the mass of planet.
Substitute
Recall the expression for radius.
Substitute
Recall the formula for the volume of a sphere.
Substitute
Recall the expression for density
Substitute
Conclusion:
The mass of Mars is
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