Gravity on extra solar planet?

Question

http://news.bbc.co.uk/2/hi/science/nature/6589157.stm

Absolutely fascinating article - I note that the world has 5 times the mass of Earth and has 1.4 times the diameter. I admit we do not know its exact chemical make-up but if we assume it is similar to Earth can someone please tell me how much higher the gravity would be.

Please show your working!

Answer 1

Let see, apply Newton's law of Universal Gravity

F=Gm1m2/r^2

G is the graviational constant

Assume m1 is you, and m2 is the planet
further, Me is mass Earth, Re is Earth's radius, Mp is the mass of the Extra Solar Planet and Rp is its radius

Therefore,

Fe= Gm1Me/Re^2

Fe is also going to equal to m1*g

m1*g=G* m1*Me/Re^2
g= G*Me/Re^2

similarly

Fp= G*m1*Mp/Rp^2

gp=G*Mp/Rp^2

Now find the ratio of the accelerations

gp/g=(GMp/Rp^2) / (GMe/Re^2)

=Mp/Me * Re^2/Rp^2
=5* (1/1.4)^2
=2.55

therefore, the acceleration of gravity would be 2.55 times bigger on the planet
since g= 9.8 m/sec^2
the g on the planet would be 25 m/sec^2

Answer 2

We do not need to know its chemical makeup. Gravity is completely independent of chemistry. So if you know the mass - 5 times earth mass, you know that the gravity for an Earth sized planet would be 5 times as much. We also know that the radius is 1.4 times larger, so that is a factor of 1.4^2 or approx. 2 smaller because of distance from the center. Put it together and you get 5/2=2.5 times the gravity on Earth. Not a nice place to be. And certainly one that one could not escape from with current rocket technology.