Question

Geostationary satellite orbits around the earth in a circular orbit of radius 36000 km. Then the time period of a spy satellite orbiting a 500 km above the earths surface (radius of earth = 6400 km) will approximately be

• A. $ \frac{1}{2}h $
• B. $ 1\,h $
• C. $ 2\,h $
• D. $ 4\,h $

Answer 1

Answer: (C)

$ {{T}_{2}}={{T}_{1}}{{\left( \frac{{{r}_{2}}}{{{r}_{1}}} \right)}^{3/2}} $ $ =24{{\left( \frac{6400}{36000} \right)}^{3/2}} $ $ =1.7h $ For spy satellite h is slightly greater than $ {{R}_{e}} $ . So, $ {{T}_{1}}>{{T}_{2}} $ hence, $ {{T}_{s}}=2h $