Question

A satellite of mass 5520 kg orbits the Earth and has a period of 6700 s . A) Determine the radius of its circular orbit. B) Determine the magnitude of the Earth's gravitational force on the satellite. C) Determine the altitude of the satellite.

Answer #1

**In an orbit**

**gravitational force provides necessary centripetal
force**

**Fg = Fc**

**G*Mm/r^2 = mv^2/r**

**v = sqrt(GM/r)**

**timeperiod T= 2*pi*r/v**

**T = 2*pi*r/sqrt(GM/r)**

**T = 2*pi*r^(3/2)/sqrt(GM)**

**r = orbital radis**

**M = mass of earth = 5.97*10^-24 kg**

**6700 =
2*pi*r^(3/2)/sqrt(6.67*10^-11*5.97*10^24)**

**orbital radius r = 7.68*10^6 m**

**(B)**

**Fc = GMm/r^2 =
6.67*10^-11*5.97*10^24*5520/(7.68*10^6)^2**

**Fc = 37266.34 N
<<<===========ANSWER**

**(C)**

**r = R + h**

**R = radius of earth = 6.37*10^6 m**

**h = r - R**

**h = (7.68*10^6) - (6.37*10^6) = 1.28*10^6 m
<<<<===========ANSWER**

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