Lesson 15 notes – Gravitational Fields

Objectives

Be able to describe how a mass creates a gravitational field in the space around it;

Be able to define gravitational field strength as force per unit mass;

Be able to use gravitational field lines to represent a gravitational field;

Outcomes

Be able to define gravitational field strength and explain that a gravitational field is a region of space around a mass that a force operates.

Be able to draw field lines that describe fields about spherical objects at a distance and close to the surface of the object. (drawings in 2D).

Gravitational Fields

All objects that have mass have an associated gravitational field. That field is greater if the mass is greater. The field gets weaker the further you are away from the mass. And the field is always attractive. If another mass enters that field it will feel a force towards the other object, just as the initial object will feel a force towards the second object because of its gravitational field.

Fields

A field in physics is defined as the force per unit …something… for gravitational fields that something is mass.

Definition

The gravitational field strength is defined as the force per unit mass. The units for gravitational field strength are therefore Nkg-1.

Field Lines

We cannot see or touch this field, but we can try to model it using field lines or lines of force. In a field line diagram, the direction of the field line at a point gives the direction of the force of attraction that would be felt by a small mass placed there. The relative density of field lines on the diagram is an indication of the strength of the field.Thus for a spherical mass, like the Earth, we would have the following diagram:

The field lines are directed radially inwards, because at any point in the Earth’s field, a body will feel a force directed toward the centre of the Earth. The field lines become more spread out as the distance from the Earth increases, indicating the diminishing strength of the field. Note that the field is really 3-dimensional, but of course on paper, we can only take a 2-dimensional slice of it. This is a radial or spherical field.

You can think of any object with mass as a gravity well distorting everything about it so that things fall toward it.

Close to the surface of the Earth, the field lines look like:

They are directed downwards (the direction in which a body near the Earth’s surface would feel a gravitational force), and they are parallel and equidistant indicating that the field is constant, or uniform.

A couple of important points to note:

  1. Field lines do not start or stop in empty space (even though on diagrams they have to stop somewhere!). They end on a mass and extend back all the way to infinity.

2.Field lines never cross. (If they did, then an object placed at the point where they crossed would feel forces in more than one direction. These forces could be resolved into one direction – the true direction of the field line there.)