A satellite with a mass of ms = 7.00 × 103 kg is in a planet's equatorial plane in a circular "synchronous" orbit. This means that an observer at the equator will see the satellite being stationary overhead (see figure below). The planet has mass mp = 8.59 × 1025 kg and a day of length T = 1.1 earth days (1 earth day = 24 hours).

Question

(a) How far from the center (in m) of the planet is the satellite?

(b) What is the escape velocity (in km/sec) of any object that is at the same distance from the center of the planet that you calculated in (a)?

Answer 1

set gravitation force equal to centripetal force

GMe*m/(r^2)=mwr where w=2PI/Period

so change T to seconds, solve for r

Answer 2

R=(G*mp*T^2/(4*pi^2))^(1/3)
Vesc=sqrt(2*mp*G/R)

Answer 3

T=24h?

Answer 4

My answer is not showing correct, using these formulas.. What am I doing wrong??

Answer 5

Is G=6.67*10^-11???

Answer 6

G is the same everywhere. Its the T that we need to input carefully.

Answer 7

My T=1.4 Earth days.. Should I convert them to seconds?? which is= 120960 sec???

Answer 8

Also which formula should I use??

Answer 9

My T is also 1.4. Someone asked me to divide that by 8.6x10^4.

Answer 10

yes @anonymous u just convert it into sec onds and solve the equation which mac has given . u'll get the right answer ..just don't forget the r^3 and t^2..yes it will give u very large numbers :( even i was obsessed . keep trying

Answer 11

@kunoi yes man..! for the b bit u have to divide the final answer by 86400 bcs 24*60*60 is 86400seconds :)