# Homework Help: Universal gravitation 9- determine the mass of planet Jupiter

1. Jun 15, 2012

### dani123

1. The problem statement, all variables and given/known data

One of the moons of Jupiter, discovered by Galileo, has an orbital period of 1.44x106s and a mean orbital radius from the centre of Jupiter of about 1.90x109m. From this information, determine the mass of planet Jupiter.

2. Relevant equations
I have made a list of equations that are relevant for this entire module on universal gravitation. So although there are many of them does not mean that they all apply in this circumstance. The ones relevant to this question will be placed in bold.

Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3

motion of planets must conform to circular motion equation: Fc=4∏2mR/T2

From Kepler's 3rd law: R3/T2=K or T2=R3/K

Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2

Newton's Universal Law of Gravitation: F=Gm1m2/d2

value of universal gravitation constant is: G=6.67x10-11N*m2/kg2

weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2

g=Gme/(Re)2

determine the mass of the Earth: me=g(Re)2/G

speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h

period of the Earth-orbiting satellite: T=2∏√R3/GMe

Field strength in units N/kg: g=F/m

Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp2

3. The attempt at a solution

Tj=1.44x106s
Rj=1.90x109m
G=6.67x10-11

with the equation highlighted above I was able to calculate the mass of Jupiter to be mj=1.96x1027kg

Does this seem like a valid answer? If anyone could check if I did this correctly or if I made a mistake and someone could point it out to me, that would be greatly appreciated! Thank you so much in advance :)

2. Jun 15, 2012

### SammyS

Staff Emeritus

The problem is similar to an earlier post of yours regarding determining the mass of Earth: https://www.physicsforums.com/showthread.php?t=613991

3. Jun 15, 2012

### grzz

Correct.

4. Jun 15, 2012

### dani123

I need to use the information provided to answer the question properly...

5. Jun 15, 2012

### dani123

Thank you grzz!

6. Jun 15, 2012

### grzz

... and I agree with the advice given to you by Doc Al in some other post to start from a very small set of basic equations and derive the required equation on the spot.

Last edited: Jun 15, 2012