# Can I assume this?

1. Jul 16, 2008

### Lance WIlliam

Space explorers land on a planet that has the same mass as Earth, but they find they weigh twice as much as they would on Earth
What is the radius of the planet?

Do I assume the 'g" = 9.8(2) ?
Since they weight twice as much...does that mean the gravity is doubled?

Im going to use the eqn. F(ma)=GMm/r^2

2. Jul 16, 2008

### Janus

Staff Emeritus
Yes, you can.

3. Jul 16, 2008

### Lance WIlliam

Can anyone plz check the math?
I get 4.50e6 which sounds right meters....
But masteringphysics is telling me im wrong
I did:

(6.67e-11)(5.98e24)/19.62=r^2

19.62 came from 9.8(2) since they wieght twice as much...

4. Jul 16, 2008

### Kurdt

Staff Emeritus
Seems ok to me.

5. Jul 16, 2008

### tiny-tim

Hi Lance!
No … you needn't assume anything about g …

this will work for any two planets of the same mass where the weight differs by a factor of 2.
ok … but you'll have to write it twice, won't you, with an r1 and an r2?

6. Jul 16, 2008

### arildno

Lance:
It just gets messy with writing digits!
Instead, use better symbols like this:
$$m_{e},r_{e},w_{e}, m$$
which means mass of earth, radius of Earth, weight on Earth and mass of explorer, respectively..
These quantities are related by the following equation:
$$w_{e}=\frac{Gm_{e}m}{r_{e}^{2}}(*)$$
On new planet "p", we also have the equation:
$$w_{p}=\frac{Gm_{p}m}{r_{p}^{2}}(**)$$
You are given the following information:
$$m_{p}=m_{e},w_{p}=2w_{e}$$
Inserting these into (**), we get:
$$2w_{e}=\frac{Gm_{e}m}}{r_{p}^{2}}(***)$$
Now, perform the division (***)/(*), and we get:
$$\frac{2w_{e}}{w_{e}}=\frac{\frac{Gm_{e}m}{r_{p}^{2}}}{\frac{Gm_{e}m}{r_{e}^{2}}}$$
which simplifies to:
$$2=(\frac{r_{e}}{r_{p}})^{2}$$
Now, you can solve this equation for the planet radius in terms of the Earth radius, only THEN introduce digits!

7. Jul 16, 2008

### Lance WIlliam

I get 4.51e6 which is still wrong.....I hate online homeowrk...:(

8. Jul 17, 2008

### alphysicist

I think that answer is correct, if the units are supposed to be meters. Are you supposed to use a different unit?

9. Jul 17, 2008

### Lance WIlliam

the units they want just say R_p_=(answer) R_e_

10. Jul 17, 2008

### Kurdt

Staff Emeritus
Ahh right that explains it. What do you multiply the Earth's radius by to get the planets radius?

11. Jul 17, 2008

### Lance WIlliam

12. Jul 17, 2008

### Kurdt

Staff Emeritus
No, the radius of the planet is definitely not twice the Earth's radius. You can work it out since you have both quantities. Just rearrange the equation in post # 9 or follow arildno's post for hints.

13. Jul 17, 2008

### Lance WIlliam

.707(R_e_) Got it.
Thankyou!