Question

A satellite of Jupiter has an orbital period of 1.77 days and an orbital of 4.22x10^5 km. Determine the mass of Jupiter.

The answer is 1.90x10^27 kg but I do not know how to solve it.

Answer 1

should the orbit be considered elliptical or circle?

Answer 2

this is what i think could be done..if the orbital is circular its length is the circumference 2*pi*r and time period=2*pi*r/orbital velocity ....from this orbital velocity could be calculated ...we know orbital velocity is v=sqrt(GM/r) then calculate mass

Answer 3

\[m = \frac{4pi^2r^3}{GT^2}\]\[m = \frac{4pi^2(4.22x10^8m)^3}{[6.674x10^{-11}N(m/kg)^2][1.77d*\frac{86400s}{d}]^2}=1.90x10^{27}kg\]Where:
m = mass of the larger object in kg
G = gravitational constant
T = orbital period of satellite (in seconds)
r = orbital distance of satellite from planet in meters

Answer 4

Sorry I typed the problem wrong. It was supposed to say and an orbital RADIUS of 4.22x10^5 km. Therefore, the orbit is a circle. Sorry about that

Answer 5

I assumed it was orbital radius before I did it :)

Answer 6

Thank you :) When you plugged in for r did you mean to write 4.22x10^5 because you wrote 4.22x10^8?

Answer 7

No...since the info you were given was in km you have to convert it to meters. I just did it on-the-fly there.

Answer 8

It must be converted to meters for the formula...so that's why I basically multiplied it times 1000.

Answer 9

Clear now or should I explain it better?

Answer 10

oh ok i get it now! Thanks so much :)

Answer 11

No problem, good luck !

Answer 12

so is my answer correct @Shane_B and @Cyn_A