# Measuring gravitational field on another plane with a pendulum

1. Apr 15, 2010

### chara76

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

T = 2pi * sqrt(L/g)

3. 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.

2. Apr 15, 2010

### collinsmark

Re: Oscillations

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.

Last edited: Apr 15, 2010
3. Apr 15, 2010

### chara76

Re: Oscillations

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?

4. Apr 15, 2010

### collinsmark

Re: Oscillations

I think you forgot to square the radius.

5. Apr 15, 2010

### chara76

Re: Oscillations

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

6. Apr 15, 2010

### collinsmark

Re: Oscillations

Looks okay to me.