Given: G = 6.672 * 10-11 N · m2 / kg2 Io, a satellite of Jupiter, has an orbital period of 1.24 days and an orbital radius of 4.11 * 105 km. From these data, determine the mass of Jupiter. Answer in units of kg.

Question

Physics

Heather Castaneda

14 February, 14:47

Given: G = 6.672 * 10-11 N · m2 / kg2 Io, a satellite of Jupiter, has an orbital period of 1.24 days and an orbital radius of 4.11 * 105 km. From these data, determine the mass of Jupiter. Answer in units of kg.

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Answers (1)

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Giada · Answer 1

Mass of Jupiter = 4.173*10^15kg

Explanation:

Using Kepler's 3rd law, it states that the orbital period T is related to the distance, r as:

T^2 = GM/4 pi * r^3

Where G = universal gravitational constant

r = radius

M = masd of jupiter

Rearranging the formular to make M the subject of formular

T^2 * 4 pi = G M * r^3

(T^2 * 4 pi) / (G * r^3) = M

(1.24^2 * 4 * 3.142) / (6.672*10^-11) (4.11*10^8) ^3

M = 19.32 / 6.672*10^-11) (4.11*10^8) ^3

M = 19.32 / 4.63 * 10^15

M = 4.173*10^15kg