Gravitational Field Question

Question

Find the value of g (gravitational field) that the moon experiences due to earth. The Earth-moon distance is 3.84 x 10⁸ meters. The mass of the earth is 5.98 x 10⁶ kilograms.

From what I understand, it should be:

g = G x m/r²

= (6.67 x 10^-11)(5.98 x 10⁶) / (3.84 x 10⁸)²

= 2.7 x 10^-21 kg m/s²

However, the actual answer is 2.7 x 10^-3 kg m/s². How?

Answer 1

A useful habit in problems like this would be the analysis of units. The units in your answer are kg*m/s². We know that this is the unit of Newtons (mass*acceleration). The equation F = Gm1m2/r² gives us the gravitational force between two bodies. I believe you're asking for the gravitational field strength, which is Newtons/kg, in other words, force/mass. This should have units of m/s².

Answer 2

You have missed a term, you need to multiply by the mass of the Moon

g = G m₁m₂ / r²