Question

What unit of force is used in the universal gravitational constant?

Answer 1

That depends on the unit system used, but in the SI (Systeme Internationale) system, units are as shown here:

The gravitational constant `G=6.67xx10^-11` `m^3 kg^-1 s^-2`. Alternatively, and equivalently, the units can be written as `Nm^2kg^-2`, in which case the force unit is the newton (N).

Explanation:

The gravitational force expression is:

`F=(Gm_1m_2)/r^2`

If we rearrange to make `G` the subject:

`G=(Fr^2)/(m_1m_2)`

We can replace the symbols with the appropriate units, as follows:

`F` `(N)`
`r` `(m)`
`m` `(kg)`

Then the units for `G` we get are `Nm^2kg^-2`.

One newton is one `kgms^-2`, which is how we translate between the two sets of units.