How do you compute an average mass for Jupiter?

In summary, Io and Europa are two of Jupiter's moons with orbital distances of 421,000 km and 671,000 km respectively and orbital periods of 1.769 days and 3.551 days. Using the equation F = GMplanetMmoon/r^2, we can compute an average mass for Jupiter by setting the mass times acceleration for each moon equal to the force exerted on it. However, the problem is that the masses of the moons and the distance between the moons and Jupiter are not given.
  • #1
Haley Feider
2
0

Homework Statement



Io and Europa are two of Jupiter's moons. Io orbits Jupiter at a distance of 421,000 km in a time of 1.769 days. Europa orbits Jupiter at a distance of 671,000 km in a time of 3.551 days. Compute an average mass for Jupiter.

Homework Equations


a=v^2/r

F=Fgravity=GMplanetMmoon/r^2

The Attempt at a Solution


I found the accelerations of the two moons however I have no idea how to use that to find Jupiters mass
 
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  • #2
I do not think we have enough information. I could be wrong though.
 
  • #3
For each moon, set its mass times acceleration equal to the force exerted on it.
 
  • #4
Mister T said:
For each moon, set its mass times acceleration equal to the force exerted on it.
The problem is, the masses are not given, and nor is the distance between the moon and Jupiter.
 
  • #5
The distances are given.
 
  • #6
Mister T said:
The distances are given.
Yes they are. My bad.
 
  • #7
thank you I will try this!
 

1. How is the average mass of Jupiter calculated?

The average mass of Jupiter is calculated using the formula M = m₁ + m₂ + ... + mₙ, where M is the average mass and m₁, m₂, ..., mₙ are the individual masses of the planet's components (such as its core, atmosphere, and moons).

2. What units are used to measure the mass of Jupiter?

The mass of Jupiter is typically measured in units of kilograms (kg) or Earth masses (M⊕). 1 Earth mass is equivalent to approximately 5.972 × 10²⁴ kg.

3. How accurate is the average mass value for Jupiter?

The average mass of Jupiter is currently estimated to be 1.898 × 10²⁷ kg with a margin of error of about 3%. This value is constantly being refined as new data and observations are gathered.

4. Can the average mass of Jupiter change over time?

Yes, the average mass of Jupiter can change over time due to factors such as the gravitational pull of its moons, collisions with other objects, and the loss or gain of atmospheric mass. However, these changes are relatively small and do not significantly affect the overall mass of the planet.

5. How does the average mass of Jupiter compare to other planets in our solar system?

Jupiter has the largest mass of any planet in our solar system, with more than twice the mass of all the other planets combined. However, compared to the Sun, Jupiter's mass is only about 0.001 times that of the Sun's. This highlights the vast difference in size and mass between a gas giant planet like Jupiter and a star like the Sun.

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