# If you halve the radius of a planet what happens to the volume/mass/density ?

1. Jan 18, 2010

### Yehia11

If you halve the radius of a planet.. what happens to the volume/mass/density ??

Okay so g on earth is about 9.8

I know that Mass = Density X Volume... so if you double the radius you quarter the "g" ?

What if you double the density and halve the radius.. can you please show me clearly using newtons equation of gravitation what happens to "g" ?

Help is very appreciated!! Thanks in advance!

2. Jan 18, 2010

### DaveC426913

Re: If you halve the radius of a planet.. what happens to the volume/mass/density ??

Is this homework? You need to show your attempts at solutions.

Note: for clarity, it will be important to distinguish between your uses of "radius".

Changing the radius of the planet will have a dramatically different result than changing the radius of (an) object's distance from the planet.

Doubling the radius of the planet itself will increase its mass (and therefore its gravitational pull) eight-fold.
Conversely, doubling the radius of an object('s distance) from the planet will quarter the gravitational pull.

And these two are not mutually exclusive. Simply standing on a planet with a doubled radius involves both of the above, so the net effect is (1/4 of 8 =) 2x gravity.

Last edited: Jan 18, 2010
3. Jan 19, 2010

### Yehia11

Re: If you halve the radius of a planet.. what happens to the volume/mass/density ??

no this isn't homework... its studying for a test. I ended up with the right answer in the exam today anyways. your answer didnt help me much, but thanks for the input anyway.

4. Jan 19, 2010

### Chewy0087

Re: If you halve the radius of a planet.. what happens to the volume/mass/density ??

Okay sure, let's call the mass of the Earth $$M_{e}$$ and mass $$R_{e}$$

We can write the mass of the Earth interms of it's density as you rightly said (density*volume, assuming the earth is spherical);

$$M_{e} = \rho \frac{4}{3} \pi R_{e} ^3$$

Note this is ONLY for the surface of the planet

$$g_{e} = \frac{\rho \frac{4}{3} \pi R_{e} ^3 G}{R_{e} ^2} = \rho \frac{4}{3} \pi R_{e} G$$

Now you can make your conclusions from here

Last edited: Jan 19, 2010
5. Jan 19, 2010

### DaveC426913

Re: If you halve the radius of a planet.. what happens to the volume/mass/density ??

Same thing. (The key is that we can guide you but not tell you.)