Question

How does gravity affect weight?

Answer 1

In a stronger gravitational field a given mass will have a larger weight.

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An object's weight is given by this equation: `w=mg`

Gravitational field strength at a distance, r, from a centre of mass is given by this equation:
`g=(GM)/r^2`

If an object is nearer a centre of mass then r will be smaller so g will be larger. In that case the weight of the object will be larger. If an object is moved from a distance R away from one centre of mass and placed a distance R away from the centre of a smaller mass then g will be smaller. In that case the weight of the object will be smaller.

A practical example: if an astronaut on earth has a weight of 833 N, on the moon he/she will have a weight of 136 N.

Using `m=w/g` the mass of the astronaut is `833/9.8=85 kg`.

So the weight on the moon (`g_M=1.6 Nkg^-1`) is: `w_M=mg_M=85×1.6=136 N`