Question

Two satellites orbit Earth at altitudes of 5200 km and 1.8×10⁴ km. What is the ratio of their orbital periods?

a) 5:3
b) 3:5
c) 2:1
d) 1:2

Answer 1

The ratio of the orbital periods of the two satellites is 3:5.

Step-by-step explanation:

To find the ratio of the orbital periods of the two satellites, we need to use Kepler's third law. According to Kepler's third law, the square of the orbital period of a satellite is directly proportional to the cube of its orbital radius. Let's denote the orbital periods of the satellites as T1 and T2, and their orbital radii as r1 and r2, respectively.

We are given the orbital radius of the first satellite as 5200 km, which means r1 = 5200 + 6380 km (accounting for the height above Earth's surface). The orbital radius of the second satellite is given as 1.8x10^4 km.

Using the ratios of the orbital radii, we can set up the following proportion: (r1^3)/(r2^3) = (T1^2)/(T2^2). Solving for the ratio of the orbital periods, we find that T1:T2 is 3:5.