Motion in a Gravitational Field

Newton's Law of Gravitation

F = GMm/r2 .... this is the attractive force between two POINT masses. G = 6.667 x 10 -11 Nm2kg-2

The point masses means that no matter how large the sphere (planets) we must include the radius of the planet in the r value.

Your weight is a force of gravitational attraction between the earth and you.

Find g using Newton's second law.

Sixty Symbols Radius of the Earth

Gravitational Field Strength

g = GM/r2 ... force per unit mass experienced at a certain point in space due to mass M.

A mass M creates a gravitational field in the space around it.

Sixty Symbols and Orbits

Orbital Motion Simulation

Gravitational Potential Energy

Ep = -GMm/r ... this is stored work in the gravitational field of the two masses at a distance r apart. If they are infinitely far apart Ep = 0.

Defined as the work done in bringing a small point mass, m, from infinity to some point P.

More explanation.

Gravitational Potential

V = - GM/r ... defined as the work done per unit mass in bringing a small point mass, m, from infinity to some point P.

Note that if we put an object of mass m at point P then the gravitational potential energy will be Ep = mV.

Q1, Q2.

Escape Velocity

Total energy of a mass m moving near a large, stationary mass M is

E = 0.5mv2 - GMm/r

Suppose that the mass m is launched with a speed of v0 away from M. Will m escape from the pull of M?

The total energy of the mass at infinity, E = 0.5mv2.

So if E > or = 0 mass escapes. So we need E = 0.5mv2- GMm/r = 0 ... and

v = root(2GM/r). Note that it is indendent of the mass of the object escaping.

Orbital Motion

Consider a planet of mass m in a circular orbit of radius r around the sun. From Newton's 2nd Law:

GMm/r2=mv2/r ... so v2= GM/r. This gives the velocity of the planet when it is in an orbit of radius r.

Period of Motion can you find it?

Equipotential Surfaces ... consist of those points that have the same potential. Similarly the distance between any two equipotential surfaces represents the same change in potential and is independent of the distance between the lines.

 

PG 153: 1, 3, 5, 7, 11, 12, 13, 23, 24, 29.

PG 131: 1 - 8.