Measuring gravitational field on another plane with a pendulum

[chara76]

Homework Statement

An astronaut arrives at a new planet, and gets out his simple device to determine the gravitational acceleration there. Prior to this arrival, he noted that the radius of the planet was 7040 km. If his 0.400-m-long pendulum has a period of 1.0 s, what is the mass of the planet?

Homework Equations

T = 2pi * sqrt(L/g)

The Attempt at a Solution

g = (4pi^2*(0.400))/1^2 = 15.79 m/2^2

I was given this equation as a hint, but I can't figure out where to go from here to get mass.

 

[collinsmark]

Newton's law of universal gravitation (equation) should get you there. Combine that with Newton's second law of motion (a = F/m) and solve for the remaining m.

 

[chara76]

Ok, this is what I get:

g = (GM)/r^2 --> 15.59=[(6.674x10^-11)(M)]/7040000

M=1.6656 x 10^18 kg

Is this correct?

 

[collinsmark]

Ok, this is what I get:

g = (GM)/r^2 --> 15.59=[(6.674x10^-11)(M)]/7040000

M=1.6656 x 10^18 kg

Is this correct?

I think you forgot to square the radius.

 

[chara76]

Thanks for catching that. How does this look?

g = (GM)/r^2 --> 15.59=[(6.674x10^-11)(M)] / (7040000)^2

M=1.17275 x 10^25 kg

 

[collinsmark]

Looks okay to me.