Gravitational fields

​​In a nutshell

Gravitational fields are force fields, where anything with a mass experiences a force. Gravitational field lines show the strength and direction of gravitational fields. 

Equations

Variable definitions

Gravitational fields

Gravitational fields are regions in space whereby anything with a mass will experience a force. 

Gravitational fields are always attractive and only objects with significant mass will have noticeable effects of gravity. 

Curiosity: Humans have mass and therefore have a gravitational field. However, it is so insignificant compared to the Earth's gravitational field, it is negligible.

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Gravitational field lines

Gravitational fields can be represented by gravitational field lines. The field lines indicate both the strength and direction of a gravitational field. 

The strength is shown by the density of field lines. The more field lines in a particular area, the greater the field strength. The direction is denoted by the direction of the arrow.

Note: As gravitational fields are always attractive, they always point towards the centre of the mass creating the gravitational field.

​​Radial fields

For celestial objects, the objects can be assumed to be point sources with radial gravitational fields. 

The further away from the object, the weaker the gravitational field as the field lines are further apart. Close to the object, the field lines are much closer, meaning the field is much stronger.

On a surface

On the surface of a celestial object, as the object is normally so large, the curvature of the object can be assumed flat.  

This means that the field lines are uniform and parallel and therefore there is a uniform gravitational field. 

Acceleration due to gravity

From Newton's second law for a constant mass, $$F=ma$$. As the acceleration is being caused by the gravitational field:

​$$F=mg$$

Rearranging for $$g$$:

​$$g=\frac Fm$$​​

​$$g$$ is the gravitational field strength of an object. Its value varies dependent on where in the gravitational field it is being measured.

Note: So far it has been assumed that $$g$$ on Earth is $$9.81 \,ms^{-2}$$. This is still a valid assumption to make as the gravitational field strength on the surface is uniform. But as the distance from Earth's surface increases, this constant can no longer be used. 

Example

A person with a mass of $$70 \ kg$$ is stood on the Moon. On the Moon, the person has a weight of $$114 \ N$$. What is the Moon's gravitational field strength?

Firstly, write down the variables. Remember the person's weight is the force exerted:

$$m = 70 \ kg \\ F = 114 \ N$$​​

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Next, state the equation needed:

$$g = \dfrac {F}{m}$$​​

Now, substitute in the values:

$$g = \dfrac{114}{70}$$​​

Calculate the final answer:

​$$g = 1.629 ... \ N \ ms^{-2}$$​​

The Moon's gravitational field strength is $$\underline{2 \ N \ ms^{-2}}$$ to one significant figure, as this is the lowest amount of significant figures given in the question.