- 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:**

**Each planet moves in an ellipse around the sun**, with the sun at one focus.**A line joining the sun to a planet will sweep out equal areas in equal times.**The square of the period of orbit is directly proportional to the cube of the radius:

**T² ∝ r**