Universal gravitation 9- determine the mass of planet Jupiter

[dani123]

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: (T_a/T_b)²=(R_a/R_b)³

motion of planets must conform to circular motion equation: F_c=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∏²K_s)*m/R²=Gm_sm/R²

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏²K_e)m/R²=Gm_em/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=F_g=m_og, where g=9.8 N/kg
F_g=Gm_om_e/R_e²

g=Gm_e/(R_e)²

determine the mass of the Earth: m_e=g(R_e)²/G

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

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

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

Determine mass of planet when given orbital period and mean orbital radius: M_p=4∏²R_p³/GT_p²

The Attempt at a Solution

T_j=1.44x10⁶s
R_j=1.90x10⁹m
G=6.67x10^-11

with the equation highlighted above I was able to calculate the mass of Jupiter to be m_j=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 :)

 

[SammyS]

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: (T_a/T_b)²=(R_a/R_b)³

motion of planets must conform to circular motion equation: F_c=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∏²K_s)*m/R²=Gm_sm/R²

Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏²K_e)m/R²=Gm_em/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=F_g=m_og, where g=9.8 N/kg
F_g=Gm_om_e/R_e²

g=Gm_e/(R_e)²

determine the mass of the Earth: m_e=g(R_e)²/G

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

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

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

Determine mass of planet when given orbital period and mean orbital radius: M_p=4∏²R_p³/GT_p²

The Attempt at a Solution

T_j=1.44x10⁶s
R_j=1.90x10⁹m
G=6.67x10^-11

with the equation highlighted above I was able to calculate the mass of Jupiter to be m_j=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 :)

"Google" the mass of Jupiter.

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

 

[grzz]

Correct.

 

[dani123]

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

 

[dani123]

Thank you grzz!

 

[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.