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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*m2/kg2. The mass of the Earth is 5.988*1024 kg. Solution

(2) Calculate the altitude at which a satellite of mass 2100 kg orbits a planet of mass 2.736*1023 kg. The gravitational force is 450 N and the universal constant of gravitation G is 6.673*10-11 N*m2/kg2. Solution

## SOLUTIONS

(1) Altitude is 36,000 km

HOW TO SOLVE THIS PROBLEM:

G = Universal constant of gravitation = 6.673*10-11 N*m2/kg2
m1 = mass of planet = 5.99*1024 kg
m2 = mass of satellite = 2105 kg
F = gravitational force = 649 N
r = altitude of satellite = ?

F= (G*m1*m2)/r2

r2= (G*m1*m2)/F

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

r= (((6.673*10-11 N*m2/kg2)*(5.988*1024 kg)*2105 kg)/649 N)1/2

r= 3.6*107 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*m2/kg2
m1 = mass of planet = 2.736*1023 kg
m2 = mass of satellite = 2100 kg
F = gravitational force = 450 N
r = altitude of satellite = ?

F= (G*m1*m2)/r2

r2= (G*m1*m2)/F

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

r= (((6.673*10-11 N*m2/kg2)*(2.736*1023 kg)*2100 kg)/450 N)1/2

r= 9.2*106 m

r= 9200 km