Question

Two satellites are in orbit around a planet. Satellite Sį two two satellite are in orbit around a planet. Satellite S1 takes 20 days to orbit the planet at
a distance of (2.0 x 10^5 km) from the center of the planet. Satellite S2 takes 160 days to
orbit the planet. What is the distance of satellite S2 from the center of the planet?

Answer 1

Answer:

8.0 x 10^-5 km

Explanation:

T1 = 20 days, r1 = 2.0 x 10^-5 km

T2 = 160 days, find r2.

By Kepler's 3-rd law, T^2 is proportional to r^3, so

T1^2/r1^3 = T2^2/r2^3

so r2 = r1*(T2/T1)^(2/3) = 2.0 x 10^-5 * (160/20)^(2/3) = 8.0 x 10^-5 km