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dani123
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Homework Statement
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.
Homework 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
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 :)