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• A-Level Physics

# Gravitational Fields

A gravitational field is a region where an object experiences a non-contact force because of its and another object’s mass. Gravitational fields are always attractive, and as such the values are always negative. Spherical objects, or things modelled as spheres such as planets and satellites, can be modelled as a point with mass at its centre.

Field Lines map gravitational fields, including their strength. The closer together, the greater the field strength. Gravitational field strength is given by:

g = F/m gravitational field strength = gravitational force / mass

## Newton's Law of Gravitation

Newton’s Law of Gravitation states that the gravitational force experienced by two objects interacting is directly proportional to the product of their masses and inversely proportional to the square of their separation:

F= −GMm/r²

Where M and m are the masses of the two objects, G is the gravitational constant, and r is the separation between the centre of the objects. This means the distance between them, plus their radii.

The gravitational field strength at a certain point from a single point mass is given as the same, divided by one of the masses:

g = −GM/r² Close to the surface of a planet, gravitational field strength can be modelled as a uniform field, and numerically equals the acceleration of free fall (9.81ms-²).

G is the gravitational constant: 6.67 E-11

## Planetary Motion

The motion of planets around their star can be described using Kepler's laws:

1. Each planet moves in an ellipse around the sun, with the sun at one focus.

2. A line joining the sun to a planet will sweep out equal areas in equal times.

3. The square of the period of orbit is directly proportional to the cube of the radius: T² ∝ r