Question

A 35 kg satellite has a circular orbit with a period of 4.7 h and a radius of 9.7 × 106 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 3.5 m/s2, what is the radius of the planet?

Answer 1

sorry my univ grav law is a little rusty so i need help. thanks

Answer 2

its cool

Answer 3

do u know the formula for the sphere

Answer 4

what specifically? is it volume, or area, or what?

Answer 5

A 20 kg satellite has a circular orbit with a period of 3.0 h and a radius of 7.5 106 m around a planet of unknown mass. If the magnitude of the gravitational acceleration on the surface of the planet is 9.5 m/s2, what is the radius of the planet?



\[g' = v^2/r = [2πr/T] ^2 /r = [2π/T] ^2 * r = 3.385e-7 r \ R^2 = [g'/g]*r^2 = [3.385e-7 /9.5]* [7.5 1e6] ^3 R= 2.06 x10^10 m \]

Answer 6

g' = v^2/r = [2πr/T] ^2 /r = [2π/T] ^2 * r = 3.385e-7 r
If R is the radius of the planet,
R^2 = [g'/g]*r^2 = [3.385e-7 /9.5]* [7.5 1e6] ^3
R= 2.06 x10^10 m

Answer 7

thst is a dif question does this help

Answer 8

im actually looking at that right now. lol

Answer 9

hope my question ab=nd answer helps u find urs

Answer 10

but im having a hard time placing variables. i mean what is r if R is radius?

Answer 11

g = G+M/R^2 to find R

Answer 12

2 steps

1) balance forces of orbit using \(m \omega^2 r_0 = \dfrac{GMm}{r_o^2}\) to find M, ie the Mass of the planet, where \(\omega = \dfrac{2 \pi}{T}\). it should lead you to \(M = \dfrac{4 \pi^2 r_o^3}{GT^2}\) but check that....

2) then use \(\dfrac{GMm}{r_p^2} = m g_p\), which is the gravity aproxination at planet surface, to find \( r_p \), ie the radius of the planet

Answer 13

hey thanks! wait i'll check to see if i can get this