Calculate Force of Gravity on Space Station at Different Distances

[mr.mair]

Homework Statement

If the Earth radius is 6.4 X 10^3 km, calculate the force of gravity on a 1.0 X 10^5 kg space station situated
(a) Earth surface
(b) 1.28 X 10^5 km from the center of the earth
(c) 3.84 X 10^5 from the center of the Earth ( about the distance to the moon)
(d) 1.5 X 10^8 km from the center of the Earth ( about the distance of the sun)

Homework Equations

Fg = mg

The Attempt at a Solution

Question a

Fg= (100000)(9.8)
Fg= 980000

questions b - d have been attemped but have no idea on these please help

 

[GRB 080319B]

Fg = mg only applies to objects less than 100 km from the Earth's surface. For b.,c., and d. you must use Fg = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are masses of Earth and satellite respectively, and r is the distance from the center of Earth to satellite.

 

[kerimek]

To calculate the force of gravity on the space station at different distances from the Earth's surface, we can use the equation Fg = (G*m1*m2)/r^2, where G is the gravitational constant, m1 is the mass of the Earth, m2 is the mass of the space station, and r is the distance between the center of the Earth and the space station.

(a) At the Earth's surface, r = 6.4 X 10^3 km, so the force of gravity would be Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(6.4 X 10^3)^2 = 980000 N, which is the same as your calculation.

(b) At a distance of 1.28 X 10^5 km from the center of the Earth, r = 1.92 X 10^5 km. Plugging this into the equation, we get Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(1.92 X 10^5)^2 = 653 N.

(c) At a distance of 3.84 X 10^5 km from the center of the Earth (about the distance to the moon), r = 3.84 X 10^5 km. Plugging this into the equation, we get Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(3.84 X 10^5)^2 = 1.77 N.

(d) At a distance of 1.5 X 10^8 km from the center of the Earth (about the distance to the sun), r = 1.5 X 10^8 km. Plugging this into the equation, we get Fg = (6.67 X 10^-11)(5.98 X 10^24)(1.0 X 10^5)/(1.5 X 10^8)^2 = 0.005 N.

As you can see, the force of gravity decreases as the distance from the Earth's center increases. This is because gravity is an inverse square law, meaning that it decreases by the square of the distance.