Universal gravitational problem

[anna sung]

Homework Statement

Planet X has a mass 8 times that of Earth and the acceleration due to gravity at its surface is 19.6 m/s2. The radius of the planet x compared to Earth is:

The answer is 2times bigger

Homework Equations

Fg = gm1m2 / r^2

The Attempt at a Solution

Is Earth's gravity 9.8 and the gravity of planet x is 19.6.
Where would I put these values in ?

 

[jedishrfu]

Check your relevant equation what do each of the variables and constants mean?

In particular, f=Gmm/r^2 where G is what?

 

[anna sung]

Check your relevant equation what do each of the variables and constants mean?

In particular, f=Gmm/r^2 where G is what?

Isn't g universal gravitational constant which is 6.67 x 10^-11?
Or is this where the 19.6m/s^2 should go into?

 

[wetlife]

G*m_1 is the acceleration due to gravity for a body

 

[ehild]

Isn't g universal gravitational constant which is 6.67 x 10^-11?
Or is this where the 19.6m/s^2 should go into?

Denote the universal gravitational constant by G. People use the notation g for the gravitational acceleration on the surface of the Earth: g≈9.81 m/s²

According to the law of universal gravitation, the force of gravity on an object of mass m is F=GmM/R² at the surface of the Earth. M is the mass of Earth (5.97 x 10^24 kg) and R is the Radius of Earth (6.37 x 10^6 m).
The gravitational acceleration is F/m=g=GM/R². Plug in the data: it is 9.81 m/s²

19.6 m/s² is the gravitational acceleration at the surface on an other planet. How does it related to the radius and mass of the planet?

ehild

 

[anna sung]

So f=mg=GmM/r^2
Then say the mass of Earth is 2. Planet x is 8 times of the earth, so then 16.
Earth has gravity 9.8 and planet x has gravity 19.6.
Then the equation is really this: g=m/r^2
So Earth is square root ( 2/9.8)=0.45
planet x is square root (16/19.6) = 0.903
Oh, okay yeah and it's twice larger.
Okay I get it,
Thank you so much.^_^

 

[ehild]

You are welcome

ehild