two satellites (same masses) orbit round Earth in radii r and 2r (from Earth's center). The closer satellite experiences force of gravity (F). What additional force (Fo) need to be added to force of gravity experienced by farther satellite so that both complete one revolution in equal amount of time.
find F0 in terms of F?
2007-12-20 05:27:57 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Physics
Bad Santa (good for me!!) your answer is correct. what i had done
F = mr w^2 & (F/4+Fo) = 2mr w^2=2F
Fo =1.75 F
thank you, confirmed
2007-12-20 06:08:29 · update #1
This question has two parts.
*First, what sort of acceleration is needed to make the two satellites revolve in the same time period
This means that they both have the same angular velocity (w).
Use the formula a=w^2*r, therefore
I'll use "f" for the far satellite and no notation for the near satellite
a = w^2*r
af = w^2 * rf
rf = 2 * r
therefore af = 2 * a
Since F=ma, Ff = 2 * F
* Second, calculate Force of Gravity on the two satellites.
Fg =G * M *m/r^2 therfore
Fg for near satellite = F
F = GMm/r^2
Fgf = GMm/rf^2
F = 4* Fgf
Fgf = 1/4 F
* Therefore,
Ff = Fo + Fgf
Fo= Ff - Fgf
Fo= 2F - 1/4 F
Fo = 1.75 F
2007-12-20 05:55:10 · answer #1 · answered by Frst Grade Rocks! Ω 7 · 3⤊ 0⤋
In order for the speeds to be equal, the force on the farther satellite must be equal to (1/2)F. This was calculated from centripetal forces.
But from Newton's Law of Universal Gravitation it is calculated that the force on the farther satellite is (1/4)F.
So the additional force that must be added is F0= (1/4)F.
2007-12-20 13:44:20 · answer #2 · answered by Anonymous · 0⤊ 2⤋