Question

A space probe is launched from Earth headed for deep space. At a distance of 10,000 miles from Earth's center, the gravitational force on it is 600lb, what is the size of the force when it is at each of the following distances from the Earths surface?

a. 20,000 miles
b. 30,000 miles
c. 100,000 miles

Answer 1

gravitational force varies based on 1/r^2

when you're double the distance =10,000 to 20,000, the force is 4 times smaller so on and so forth.

As force is proportional to 1 / {distance squared}, the force will be 1 / 2^2 (i.e. 1/4) of the force at the reference distance (i.e. 1/4 * 600 = 150 lb)

Answer 2

Grav Force = GMm/r squared. M is earth's mass. m is the probe. r is distance to centre of earth.Given that 600 = GMm/(10,000^2).GMm = 600x(10,000^2) for 10, 000 milesGMm = ? x (20,000^2) for 20, 000 milestherefore600x(10,000^2)=? x (20,000^2)therefore [600x(10,000^2)]/(20,000^2)=? [600x(1x1)]/(2x2)=? [600/4]=? ?=150lb.Same procedure for b and c.Please ask if you want further help.