Question

as a rocket carrying a space probe acceleraes away from earth the fuel is being used up and the rocket's mass becomes less when the mass of a rocket(and its fuel) is M and the distance of the rocket from eart's centre is 1.5rE, the force of gravitational attraction between eartrh and rocket is F1, when some fruel is consumed causing the mass to become 0.5M and the distance from Earth's centre is 2.5rE the new gravitational attraction is F2. Determine the ratio of F2 to F1. Tkhe symbalrE is earth's radius.

Answer 1

The earth's gravity reaches out forever but the force of attraction on bodies at great distances would be extremely small depending on the mass of the body. The Law of Universal Gravitation states that each particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Expressed mathematically,
F = GM(m)/r^2
where F is the force with which either of the particles attracts the other, M and m are the masses of two particles separated by a distance r, and G is the Universal Gravitational Constant. The product of G and, lets say, the mass of the earth, is sometimes referred to as GM or µ (the greek letter pronounced meuw as opposed to meow), the earth's gravitational constant. Thus the force of attraction exerted by the earth on any particle within, on the surface of, or above it, is F = 1.40766x10^16 ft^3/sec^2(m)/r^2 where m is the mass of the object being attracted = W/g, and r is the distance from the center of the earth to the mass.

F1 = GMm1/r1^2
F2 = GMm2/r2^2

F2/F1 = [GMm2/r2^2]/[GMm1/r1^2]
......= m2(r1^2)/m1(r2^2)