(This a question based out of the Textbook \"Universe\" chapter 4 box 4-4) There

Question

(This a question based out of the Textbook "Universe" chapter 4 box 4-4)

There is no simple property of the light that we receive from a celestial body that would allow us to directly estimate that body's mass. However, as shown in Box 4-4 of Universe, we can instead determine quite accurately the masses of celestial bodies by studying how objects orbit about them. The example in box 4-4 shows how to find the mass of Jupiter, based on two easily measured properties of the orbit of its moon Io: The orbital period of Io The average distance from the center of Jupiter to the orbit of Io. Here, we will use exactly the same procedure to estimate the mass of Saturn, based on the orbit of its largest moon, Titan. That is, estimate the mass Saturn, given that Titan's average orbital distance is 1; 221; 870 km; and its orbital period is 15:945 days

Explanation / Answer

circumference = 2 x pi x r = 2 x 3.14 x 1221870 = 7673343.6 x 103 m

T = 15945 days = 15945 x 24 x 60 x 60 seconds = 1377648 x 103 seconds

velocity = circumference/T = 5.5698 m/s

M = 4pi2r3/GT2= 3.794531918 x 1010 / G = 3.794531918 x 1010/6.674 x 10-11

M = 0.568554377 x 1021 kg = 5.68554377 x 1020 kg

in case of any doubt, please comment

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.