Homework Soursea Using the average radius of the Earth in your calculations
a) Using the average radius of the Earth in your calculations determine the magnitude of Earth\'s gravitational field for a 70.0-kg person standing at Earth\'s surface.
b) Using the average radius of the Earth in your calculations determine the magnitude of Earth\'s gravitational field for a 700.0-kg satellite in orbit 180 km above Earth\'s surface.
c) Using the average radius of the Earth in your calculations determine the magnitude of Earth\'s gravitational field for the Moon (use 3.844 × 108 m for the center-to-center distance between Earth and the Moon).
Solution
(a).Mass of person m = 70 kg
The magnitude of Earth\'s gravitational field for a 70.0-kg person standing at Earth\'s surface is
F =GM/R 2
Where G = Gravitational constant = 6.67 x10 -11 Nm 2/kg 2
M = Mass of earth = 5.972 x10 24 kg
R = Radius of earth = 6.37 x10 6 m
Substitute values you get , F =(6.67 x10 -11)(5.972 x10 24 ) /(6.37 x10 6) 2
= 9.816 m/s 2
(b).Mass m = 700 kg
Height of the satellite above the earth surface h = 180 km = 180 x10 3 m
The magnitude of Earth\'s gravitational field for a 700.0-kg satellite in orbit 180 km above Earth\'s surface is
F =GM/(R+h) 2
Where G = Gravitational constant = 6.67 x10 -11 Nm 2/kg 2
M = Mass of earth = 5.972 x10 24 kg
R = Radius of earth = 6.37 x10 6 m
Substitute values you get , F =(6.67 x10 -11)(5.972 x10 24 ) /[(6.37 x10 6)+(180x10 3)] 2
= 9.284 m/s 2
(c).Distance between center to center distance between earth and the moon is r = 3.844x10 8 m
Radius of moon R \' = 1.737x10 6 m
the magnitude of Earth\'s gravitational field for the Moon F =GM/(r-R) 2
Where G = Gravitational constant = 6.67 x10 -11 Nm 2/kg 2
Substitute values you get , F =(6.67 x10 -11)(5.972 x10 24 ) /[(3.844x10 8)-(1.737 x10 6)] 2
= 2.72 x10 -3 m/s 2
