In Gulliver\'s Travels, Jonathan Swift wrote about a country where astronomers h

Question

In Gulliver's Travels, Jonathan Swift wrote about a country where astronomers had found that Mars had two moons. (The moons of Mars were unknown at that time.) "They have likewise discovered two lesser stars, or satellites, which revolve about Mars, whereof the innermost is distant from the center of the primary planet exactly three of his diameters, and the outermost five; the former revolves in the space of ten hours, and the latter in twenty-one and a half..." If this information were correct, what would the mass of Mars be? The radius of Mars is 3,393,500 m and G=6.67x10^-11

Explanation / Answer

the accleration due to gravity on the mars is

g = GM/ r^2

M = gr^2/ G

= (3.73) ( 3393500)^2/6.67 * 10^-11

= 6.45 × 10^23 kg

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