3.4 Gravitational Field and Potential

Question 1

What is the gravitational potential?

Answer 1

The gravitational potential energy per unit mass at that point. It is the work done in moving the unit mass from infinity to that point.

Question 2

What is the gravitational potential energy (or the change in it) in a uniform field?

Answer 2

Vgrav = g x change in h

Question 3

What is the equation for the gravitational potential in a radial field?

Answer 3

Vgrav = - Gm/ r

Question 4

Why are the units of both Jkg^-1?

Answer 4

Because the gravitational potential is the potential per unit mass (hence it needs to be multiplied by mass to find energy )

Question 5

Why is the gravitational potential energy negative?

Answer 5

Since we have to do work against the gravitational field to move an object out of it. The further we are away from point mass the smaller the magnitude of Vgrav.

Question 6

The earth feels a force due to the fact it is in the gravitational field of what?

Answer 6

The sun

Question 7

How can we work out the force between sun and earth?

Answer 7

Using newton’s law of gravitation.

Question 8

Why does the earth have centripetal force?

Answer 8

Since it is orbiting the sun

Question 9

How can we work out the orbital speed/ veloctity of the earth?

Answer 9

Equaling those two together (centripetal force and newtons law of gravitation) to give v = (square root)GM/r

Question 10

What is the equation for find the period T?

Answer 10

T^2 = (4π^2/GM)r^3

this is rearranging kepler’s third law (subsituting T = 2 π/v into v^2 = GM/r)