Gravitational force between point masses (13.2)

What is Newton’s law of gravitation?

Newton’s law of gravitation - gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of separation

What is the equation relating to Newton’s law of gravitation?

F = GMm/r²

Where F is gravitational force (N)

Where G is the gravitational constant (Nm²kg^-2) - 6.67 ×10^-11

Where M is the mass of one of the point masses (kg)

Where m is the mass of the other point mass (kg)

Where r is the separation between the point masses (m)

What is the centripetal force for a body in a circular orbit in a gravitational field?

For a body orbiting in a circular orbit in a gravitational field the centripetal force is the gravitational force

What is the relations can be derived from the fact F_c = F_g for a body in circular orbit in a gravitational field?

F_g = F_c

GMm/r₂ = mv²/r = mrω²

v² = GM/r

ω² = GM/r³

T² = 4Π²r³/GM

Where v is the linear velocity of the body in orbit (ms^-1)

Where G is the gravitational constant (Nm²kg^-2) - 6.67 ×10^-11

Where M is the mass of the body being orbited (kg)

Where r is the distance between the body in orbit and the body being orbited (m)

Where ω is angular velocity (radss^-1)

Where T is the period of orbit (s)

What is a geostationary orbit?

A geostationary orbit is an orbit in which:

• The satellite has a orbit period equal to the Earth’s rotational period (24 hours)

• Moves in the same direction Earth spins

• Remains directly above the equator (so it always orbits the same point above the Earth’s surface)