We know that the gravitational force of attraction keeps the moon revolving around the earth, and the earth revolving around the Sun. However, recall that for the moon to escape the bound of the earth’s gravitational force and fall under the influence of the Sun’s gravity, it must possess a certain velocity. This is what is known as escape velocity.

Determine a relation for the escape velocity by equating the centripetal force of attraction between the moon and the earth and the gravitational...

Formula Setup:

• g at height h from the Earth's surface = g' = g (R/(R+h))^2
• g at depth h below the Earth's surface = g' = g(1 - h/R)

To find: h where g' = g/4

At height h above the Earth's surface:

g' = g(R/(R+h))^2

g/4 = g (R/(R+h))^2

1/4 = (R/(R+h))^2

1/2 = R/(R+h)

R + h = 2R

h = 2R - R

So, h = R

At depth h above the Earth's surface:

g' = g (1 - h/R)

or, g/4 = g (1 - h/R)

or, 1/4 = 1 - h/R

or, h /R = 1- 1/4

or, h/R = 3/4

So, h = 3R/4

Hence, at height h = R above the Earth's surface and at a depth h = 3R/4...

A hypothetical point at which the whole mass of a body is considered to be concentrated is known as centre of mass.

While the hypothetical point at which whole weight of a body is considered to be concentrated is known as centre of gravity.

As we know weight is g times the mass of the body and g decreases with altitude, if we ignore this variation of g over the vertical dimension of body(I e. in uniform gravitational field), then it's centre of mass and centre of gravity will be equal.

The gravitational potential energy of a voyager of mass m at a distance r from the earth iswhere M is the mass of the earth. The gravitational potential energy of the voyager at a distance r from the moon is where M_moon is the mass of the moon. As r and m are constants and M > M_moon, then numerically, W > W_moon, i.e. the work needed to make a voyage from the earth to the moon is greater than that from the moon to the earth. So it takes more fuel to make the voyage from the earth to the...

Gravity is just another name for Gravitation. However, it differs from Gravitation in a sense that it is an attractive force between a very large and a very small body. For example: the attraction between the Earth and a body is called gravity because the mass of Earth is very much greater than that of the body.

The centre of gravity of a body is defined as the point where the whole weight of the body can be supposed to act.

The centre of mass of a body is the point the where the whole mass of the of the body can be supposed to be concentrated.

For regular bodies, the C.G and C.M. coincide but, for a body of large dimension. The value of g is different for its different parts, the C.M may not coincide with C.G. At a gravity free space, C.G. makes no sense but C.M. has still meaning.

The weight of an object or entity, in the physical sense, would generally become zero under the circumstances of being in a weightless environment, such as in outer space or during freefall.