Gravitational Fields

What is a force field?

A region where an object experiences a non contact force

They cause interactions between particles or objects

What do gravitational fields act on?

Any object with a mass

Larger masses experience a greater force

Force of gravity equation

(GM1M2)/r^2

Always attractive

What is a point mass?

A theoretical object that has a mass but no dimensions

What does it mean when an object/sphere acts as a point mass?

We assume all their mass is concentrated in their centre

What shape is the gravitational field of earth?

• Radial field

• However if we are close to the ground it is almost exactly uniform so we can assume this

• Fields lines are almost parallel

Law of universal gravitation

• An inverse square law

• F proportional to 1/r^2

  

Gravitational field strength

Force per unit mass

g = Fm

• this changes depending on where you are in the field

• At the earth’s surface = 9.81N/kg

• g = Fm → F = mg = ma

• In a radial field g is inversely proportional to the square of r

• Combine F equation and g equation you get GM/r^2 = g

How does the gravitational field strength change with distance from the centre of the earth?

• from the centre to the surface, g is proportional to distance (linear relationship)

• from the surface outwards, g is inversely proportional to r^2

Gravitational potential

Work done to move a unit mass from infinity

• at a point = GPE/ m

• In a radial field V(grav)= -Gm/r

• It is negative as you do work against the field to move the object out of it

just think of it as the work need to pull something away from the other to infinity

• further away it is easier to as the strength of gravity is less

Similarities between gravitational and electric fields

• they both follow inverse square laws

• the negative radial field is the same as the radial field of gravity

• gravitation potential and electric potential are both 0 at infinity

Differences between gravitational and electric fields

• gravitational fields act on masses while electric fields act on charges

• gravitational forces are always attractive, electric can be attractive or repulsive

• objects can be shielded from electric fields but not gravitational fields

• the magnitude of an electric force depends on the medium between the two charges whereas gravitational forces don’t

Orbits

• Speed depends on the radius of the orbit and the mass of the larger body

• Circular motion caused by a centripetal force of gravity

• The orbiting object will constantly change direction so it is accelerating

How can you find the speed of an orbit?

combine the centripetal force equation with the gravitational force equation

Rearrange to find v

V = square root of GM/r

How can you find the period of an orbit?

Use the equation T=2(pi)r/v from circular motion

Combine with v = square root of GM/r

You get

T^2 = (4(pi^2)/GM)r^3