Weather Satellites and Orbits

# Problems and Solutions

## Newton's Law of Gravity

(1) Calculate the altitude at which a satellite of mass 2105 kg orbits the Earth.
The gravitational force is 649 N and the universal constant of gravitation G is 6.673*10^{-11} N*m^{2}/kg^{2}.
The mass of the Earth is 5.988*10^{24} kg. Solution

(2) Calculate the altitude at which a satellite of mass 2100 kg orbits a planet of
mass 2.736*10^{23} kg. The gravitational force is 450 N and the universal constant
of gravitation G is 6.673*10^{-11} N*m^{2}/kg^{2}. Solution

**SOLUTIONS **

**(1) Altitude is 36,000 km**

HOW TO SOLVE THIS PROBLEM:

G = Universal constant of gravitation = 6.673*10^{-11} N*m^{2}/kg^{2}

m1 = mass of planet = 5.99*10^{24} kg

m2 = mass of satellite = 2105 kg

F = gravitational force = 649 N

r = altitude of satellite = ?

F= (G*m1*m2)/r^{2}

r^{2}= (G*m1*m2)/F

r= ((G*m1*m2)/F)^{1/2}

r= (((6.673*10^{-11} N*m^{2}/kg^{2})*(5.988*10^{24} kg)*2105
kg)/649 N)^{1/2}

r= 3.6*10^{7} m

**r= 36,000 km**

**(2) Altitude is 9230 km**

HOW TO SOLVE THIS PROBLEM:

G = Universal constant of gravitation = 6.673*10^{-11} N*m^{2}/kg^{2}

m1 = mass of planet = 2.736*10^{23} kg

m2 = mass of satellite = 2100 kg

F = gravitational force = 450 N

r = altitude of satellite = ?

F= (G*m1*m2)/r^{2}

r^{2}= (G*m1*m2)/F

r= ((G*m1*m2)/F)^{1/2}

r= (((6.673*10^{-11} N*m^{2}/kg^{2})*(2.736*10^{23} kg)*2100
kg)/450 N)^{1/2}

r= 9.2*10^{6} m

**r= 9200 km**

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