Sun and Earth Mass, Distance, and Center-of-Mass Problem: Exam Sample

[quickclick330]

More sample exam problems...

2) The mass of our sun is ~ 2 x 10^30 kg. The mass of a planet is 6 x 10^24 kg. If the
distance between the center-of-mass of each is 100 x 10^11 m, what is the distance
in meters from the center-of-mass of the sun to the center-of-mass of the Sun-
Earth system?

What should I use to go about this problem? Thanks!

 

[temaire]

Well, you could start by writing down some relevant formulas, such as:

$$F_{g} = \frac{Gm_{1}m_{2}}{r^{2}}$$

$$\frac{T_{A}^{2}}{r_{A}^{3}} = \frac{T_{B}^{2}}{r_{B}^{3}}$$

 

[quickclick330]

What is the second equation? I'm not familiar with that one.

 

[Telmerk]

That is the third law of Johannes Kepler. ;-)
r: sun-planet distance
T: period

 

[quickclick330]

That one would help. So how would you relate them together? Energy Principle?

 

[rock.freak667]

The second equation is what happens as a result of some fancy manipulation of centripetal force and gravitational force of attraction.

 

[quickclick330]

ooh okay. I went to a help center and we had the centripetal force and gravitational force set equal to each other but the grad TA couldn't figure out how to get rid of velocity. So that second equation is really all i need right?

 

[rock.freak667]

Use the centripetal force as $m\omega^2r$ where $\omega=\frac{2\pi}{T}$ to not have v and have the period of revolution

 

[quickclick330]

will r be the distance from planet to center of mass?

 

[Telmerk]

Yes.

 

[D H]

I realize this is too late, but the help here has been quite bad. There is no need to invoke any of Kepler's laws to solve this problem. This is a simple problem. Quickclick, what is the equation of the center of mass for a group of particles?