Universal gravitation 9- determine the mass of planet Jupiter

In summary, using Kepler's 3rd law and the equation for gravitational force of attraction between a planet and its orbiting satellites, we can determine the mass of planet Jupiter to be approximately 1.96x10^27 kg.
  • #1
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 :)
 
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  • #2
dani123 said:

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 :)
"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
 
  • #3
Correct.
 
  • #4
I need to use the information provided to answer the question properly...
 
  • #5
Thank you grzz!
 
  • #6
... 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:

1. How is universal gravitation related to determining the mass of Jupiter?

Universal gravitation is a fundamental force of nature that governs the interactions between all objects with mass. It allows us to calculate the gravitational force between two objects based on their masses and the distance between them. By using this formula and measuring the gravitational force between Jupiter and its moons, we can determine the mass of Jupiter.

2. What is the formula for universal gravitation?

The formula for universal gravitation is F = G (m1m2/r^2), where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

3. How is the mass of Jupiter calculated using universal gravitation?

To calculate the mass of Jupiter, we first measure the gravitational force between Jupiter and one of its moons using the formula F = G (m1m2/r^2). Then, we rearrange the formula to solve for the mass of Jupiter (m1) by plugging in the known values for G, the distance between Jupiter and its moon, and the known mass of the moon (m2).

4. What is the gravitational constant and why is it important in determining the mass of Jupiter?

The gravitational constant, denoted by G, is a fundamental constant that represents the strength of the gravitational force between two objects. It is important in determining the mass of Jupiter because it allows us to calculate the gravitational force between Jupiter and its moons, which is necessary for determining Jupiter's mass.

5. Are there any other methods for determining the mass of Jupiter?

Yes, there are other methods for determining the mass of Jupiter, such as using Kepler's laws of planetary motion or analyzing the gravitational effects on other objects in the solar system. However, using universal gravitation is one of the most accurate and commonly used methods for determining the mass of Jupiter.

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