Calculating Gravitational Field Strength

Deriving and using the equation for gravitational field strength.


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Up Learn – A Level physics (aqa)

Gravitational Force and Field

We’ve seen that gravitational force can be calculated using Newton’s Equation, which is…

Newton’s equation for gravitational force is this. 

And we’ve also seen that the gravitational field strength is defined as the gravitational force per unit mass.

And that means per unit mass of a test mass. 

So now, if we rearrange this [F=GMm/r2], to get Force divided by the mass of the test mass…

… we get this. [F/m=GM/r2]

And we call this the gravitational field strength, g. 

So gravitational field strength equals GM/r2

… and the units are newtons per kilogram. 

Just like in Newton’s equation, the distance r is measured from the centre of each mass.

Now, this equation tells us that an object with a larger mass will have… 

An object with a larger mass will have a stronger gravitational field around it

And the further we move away from that mass…

The further we move away from the source mass, the weaker the gravitational field will get. 

So why is it useful to be able to calculate gravitational field strength?

Well, firstly, if we know the gravitational field strength at a point, we can find the size and direction of the gravitational force easily for any mass at that point.

For instance if a comet is at this position in the sun’s gravitational field…

… where the gravitational field strength is this…

The gravitational force experienced by the comet is 1.5 times 10 to the 17 Newtons. [1.5 x 1017 N] 

Secondly, we can also look at how gravitational field strength varies at different positions around a mass.

And this can tell us a lot about how masses will move within that gravitational field.

Which is exactly what Matt Taylor and his team did when they were looking for the Philae lander!

Finally, you’ll have used a lower case g many times before, in mechanics.

There, we said that g was the acceleration due to gravity which is 9.81 meters per second squared.

Or we could use the equivalent units, newtons per kilogram instead. [N kg-1]

However, back then, we were only doing calculations on or around the Earth’s surface.

But we know that all objects with mass exert a gravitational field across far longer distances than we covered in mechanics.

So we’re going to look at calculating the gravitational field strength at different positions.

So, in summary… 

The equation for gravitational field strength is…

The equation for gravitational field strength is this. [g=GM/r2]

And gravitational field strength is…

Gravitational field strength is a vector with a direction towards the source mass.

Finally, we always measure the distance, r from…

We always measure the distance, r, from the center of each mass.