Silly Gravity / Radius Question

[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

 

[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

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

 

[mathman]

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