Posted by Roberto on Saturday, May 7, 2011 at 5:18pm.
well, centripetal force= gravityforce from Earth-Gravityforce from Moon
mV^2/Rs=GMem/Rs^2 -GMm*m/(Rm-Rs)^2
where Rs is the orbital distance from earth, Rm is the moon orbital distance.
Now, change to period: 2PI*Rs/Period= V
(2PI)^2*Rs/Period^2=GMe/Rs^2-GMm/(Rm-Rs)^2
Lets look at the period of the moon:
(2PI)^2 Rm/Period^2=GMmMe/Rm^2
or 1/period^2= GMmMe/Rm^3 * 1/(2PI)^2
put that into the equation...
Rs*GMmMe/Rm^3=GMe/Rs^2-GMm/(Rm-Rs)^2
Let Mm/Me = r= ratiomasses
Rs/Rm^3= (1/r)/Rs^2-r/(Rm-Rs)^2
Rs=Rm^3/rRs^2 -r Rm^3/(Rm-Rs)^2
Rs^3=Rm^3/r- rRm^3 (Rs^2/(Rm-Rs)^2)
I think I would turn to a graphical solution at this point.
double check my work. Something is bothering me about this.
The answer I posted previously is wrong. See instead
http://www.ottisoft.com/Activities/Lagrange%20point%20L1.htm
Related Questions
Physics - A satellite is placed between the Earth and the Moon, along a straight...
Physics - A satellite is placed between the Earth and the Moon, along a straight...
physics - magine a straight line connecting the centers of the earth and the ...
physics help please! - A spacecraft is on a journey to the moon. At what point...
PHYSICS - Consider a spaceship located on the Earth-Moon center line (i.e. a ...
physics hey damon one more please! =] - Consider a spaceship located on the ...
physics - still cant get this one? so damon i know you wanna help! or anyone ...
Physics - Consider a spaceship located on the Earth-Moon center line (i.e. a ...
Physics - Consider a spaceship located on the Earth-Moon center line (i.e. a ...
Physics - Given that the distance between the Earth and the Moon is d = 3.84 x ...
For Further Reading
