General Gravitational Law

It was said that newton thought of gravitational forces when he noticed an apple falling down from a tree towards the ground , so Newton suggested some basic concepts which helped up in setting the general gravitational law

1- The Apple fell down due to the gravitation of Earth and in turn , it attracted Earth towards it (According to Newton’s third Law).

2- The Gravitational attraction between diffrent bodies occurs even if they are far apart from each other such as : the attraction between moon and earth and the attraction between sun and planets.

3- The gravitational attraction between bodies depends on The mass of bodies and the distance between them.

Deduction of general Gravitational law :

It could be verified practically and theoritically that the gravitational attraction force between two bodies is: Directly proportional to the product of their mass F ∝m1*m2——————(1) Inversly Proportional to the square of distance between them. F ∝ 1/d^2—————-(2)

From (1) and (2) :

F ∝ m1*m2/d^2

therefore : F = G *m1*m2 / d^2

where G is the universal gravitational constant

G=6.67 * 10^-11 Nm^2/Kg^2

The universal gravitational constant is the attractive force between two 1 Kg spherical bodies whose centers are one meter apart .

G = F*d^2 /m1m2

Why are astronauts weightless in space?

imagine a girl in an elevator so :

the gravity pulls down the girl , the girl pulls on the elevator’s surface

the elevator has a reaction opposite in direction which is the tension force.

1- When the elevator is at rest :

since the acceleration= zero

therefore :

F net =Ft-Fg = ma

where Ft is the tention force

(normal force in an elevator)

F net = Ft-Fg= zero

therefore Fg=Ft.

2- When the elevator moves upwards by

acceleration (a) :

since the elevator is moving upwards

therefore the force of gravity has a negative

sign

F net =Ft-Fg = ma

therefore

Ft = Fg + ma

and since the tension force is greater than gravity so the girl feels heavier in this case.

3- When the elevator is moving downwards by acceleration (a) :

since the motion is upwards , therefore the force of gravity has a positive sign while the tension force – which is opposite to gravity- has a negative sign thus we have :

F net =Fg-Ft = ma

therefore -Ft=-Fg+ma

therefore Ft = Fg-ma

therefore tension force is smaller than gravity so the girl feels lighter .

4- Imagine that the cable of elevator is cut and the elevator is falling freely :

Ft = Fg-ma

and since the elevator is moving with the same acceleration due to gravity :

therefore Ft = Fg-mg

and since Fg=mg

Therefore Ft = Zero

and since the the tension force is zero therefore the girl feels weightless

this is the same reason for why are astronauts are weightless in space , they feel weighless not because gravity doesn’t exist in space (of course gravity does exist in space), but because they are falling freely towards earth’s center.

The normal force is the responsible for the feeling of weight and in the absence of this force we feel weighless.