Question

A rocket is fired from earth towards sun. Justify that acceleration due to gravity does not depend on mass of the rocket moving? Is the acceleration due to gravity on rocket at a point above earth, inversely related with square of distance of that point from earth? Explain shortly. Using the following data, how would you determine the point where the gravitational force on the rocket is zero? [ Note: neglect the attractive forces of other planets on the rocket]

[Given: Mass of Sun= 2X1030 kg, mass of Earth= 6 X 1024 kg, Orbital radius of earth to sun,

R =1.4 x1011 m]. This Gravitational force is very weak force, but still it is considered the most important force in nature. Explain why?

Answer 1

let mass of rocket be :m

let mass of earth be :M

Force of gravitation between earth and rocket is

where R distance between rocket and the centre of earth

G is for gravitational force constant

Force by rocket , F=ma ......a is acceleration , it is acceleration due to gravity g

g = F/m

this is shows that acceleration due to gravity does not depend on the mass of the rocket and is inversely proportional to the square of the distance between earth centre and the rocket.

now our rocket is moving from earth to sun , so lets tale only these 3 things in our picture, rocket, earth, sun.

when the rocket is in space, the earth is also applying gravitational force on it and sun as well, but at one point, the gravitational force between rocket and earth will be equal to the gravitational force between rocket and sun and both force has opposite direction, so due to that,we can say gravitational force between earth is zero as it is balanced by sun's gravitational force.

let be the mass of sun.

let R be the distance between sun and earth

let r be the distance of rocket from the earth.

so distance between rocket and sun will be : (R-r)

lets find value of r

taking square root on both side

so , from that much distance from earth, the force will be zero.

and Gravitational force plays an important role for initiating the birth of stars, for controlling the entire structure of the universe and evolution of the universe. If helped to explain many natural phenomena. also, its is long-distance force without distance limit. so it is very important.