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 = 6.67 x 10^-11 N·m²/kg². A) 3.86 × 10²⁴ kg B) 6.45 × 10²³ kg C) 5.67 × 10²¹ kg D) 2.83 × 10²¹ kg E) 4.78 × 10²⁰ kg

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Quizplus · Accepted Answer

The correct answer is A because the mass of Mars can be calculated using the formula for the orbital period of a satellite:T^2 = (4π^2/GM) * r^3where T is the orbital period, G is the gravitational constant, M is the mass of the central body, and r is the distance from the central body to the satellite.We can use the given information to find the mass of Mars:T1 = 10 hours = 36000 secondsr1 = 3 * 3,393,500 m = 10,180,500 mT2 = 21.5 hours = 77400 secondsr2 = 5 * 3,393,500 m = 16,967,500 mSubstituting these values into the formula, we get:36000^2 = (4π^2/G * M) * 10,180,500^377400^2 = (4π^2/G * M) * 16,967,500^3Dividing the second equation by the first equation, we get:(77400/36000)^2 = (16,967,500/10,180,500)^3Solving for M, we get:M = 3.86 × 10^24 kg

In Gulliver's Travels, Jonathan Swift Wrote About a Country Where