# Silly Gravity / Radius Question

1. Sep 30, 2004

### atrain77a

I think this is pretty basic, but I'm obviously missing something. Here's the ?:

A planet has the same mass as earth, but it's gravitational acceleration is g/2. What is the radius of the planet?

What's the relationship here? -AT77A

2. Sep 30, 2004

### Pyrrhus

Well, let me see (correct me if i'm wrong)

$$\vec{F} = G \frac{m_{1}m_{2}}{r^2} \vec{r}$$

$$m_{2} \vec{g} = G \frac{m_{1}m_{2}}{r^2} \vec{r}$$

$$\vec{g} = G \frac{m_{1}}{r^2} \vec{r}$$

so, if g/2

$$\frac{\vec{g}}{2} = \frac{G \frac{m_{1}}{r^2}}{2} \vec{r}$$

3. Oct 1, 2004

### mathman

For a constant mass, to cut g in half, you have to increase the radius by 1.414... (sqrt(2)).