Question

What is the radius of a communications satellite’s orbital path that is in a uniform circular orbit around Earth and has a period of exactly 24.0 hours (86,400 seconds). (Measurement is from the center of Earth.)

Answer 1

What is the radius of a communications satellite’s orbital path that is in a uniform circular orbit around Earth and has a period of exactly 24.0 hours (86,400 seconds). (Measurement is from the center of Earth.) A. 6.5 × 10^4 m B. 3.8 × 10^5 m C. 4.2 × 10^7 m D. 9.5 × 10^7 m

Answer 2

Answer:

42400 km

Explanation:

The time taken by a satellite to complete one revolution around the earth is called the time period of the satellite.

The time period for the satellite is given by

$T = \frac{2\pi }{R}\times \sqrt{\frac{(R+h)^{3}}{g}}$

where, R be the radius of earth, h be the height of satellite from earth's surface and g be the acceleration due to gravity.

Substitute, 86400 s for T, 6400000 m for R and 9.8 m/s^2 for g , we get

$86400 = \frac{2\pi }{6400000}\times \sqrt{\frac{(6400000+h)^{3}}{9.8}}$

h = 35954355.13 m

h = 36 x 10^3 km

Distance from the centre of earth is R + h = 6400 km + 36000 km = 42400 km .