Radius of Planet with Double Gravity: Calculating with F=ma

[Lance WIlliam]

If the question reads:
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

 

[Janus]

Yes, you can.

 

[Lance WIlliam]

Can anyone please check the math?
I get 4.50e6 which sounds right meters...
But masteringphysics is telling me I am 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...
Thankyou for your help.

 

[Kurdt]

Seems ok to me.

 

[tiny-tim]

Hi Lance!

Do I assume the 'g" = 9.8(2) ?

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.

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

ok … but you'll have to write it twice, won't you, with an r₁ and an r₂?

 

[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!

 

[Lance WIlliam]

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

 

[alphysicist]

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

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

 

[Lance WIlliam]

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

 

[Kurdt]

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

 

[Lance WIlliam]

So my (answer) times 2?

 

[Kurdt]

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.

 

[Lance WIlliam]

.707(R_e_) Got it.
Thankyou!