Question

Show with proof, the planet which an astronaut would have a greater weight if Planet A has twice the mass and twice the radius of Planet B.

Answer 1

First let's look at the gravitational formula by newton:

`f = g * \frac{m1 * m2}{ {r}^(2) }`

Now the f and g should be capital but that's not possible with the equation system. But we can see that the force the astronaut is pulled at is dependent on the mass and the distance if we assume his mass stays the same (mass and weight aren't the same also g is a constant). If a planet has twice the radius the force will by four times as weak because of the ^2. This is not compensated by the twice as big mass. Therefore the astronaut will have a higher force and thus a higher weight on planet B