Gravity and mass with Jupiter's moons

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SUMMARY

The discussion focuses on calculating the mass of Jupiter using data from its four largest moons: Io, Europa, Ganymede, and Callisto. The gravitational force equation, g1 = G((m1m2)/r^2), is utilized to derive Jupiter's mass from each moon's orbital characteristics. The results obtained from each moon's data are compared for consistency, emphasizing the importance of using Kepler's laws and principles of Uniform Circular Motion in these calculations.

PREREQUISITES
  • Understanding of gravitational force equations, specifically g1 = G((m1m2)/r^2)
  • Familiarity with Kepler's laws of planetary motion
  • Knowledge of Uniform Circular Motion principles
  • Basic understanding of celestial mechanics and orbital dynamics
NEXT STEPS
  • Research how to apply Kepler's Third Law to calculate planetary masses
  • Study the concept of gravitational acceleration and its calculation
  • Explore the relationship between orbital period and distance in celestial mechanics
  • Learn about the implications of mass measurements in astrophysics
USEFUL FOR

Astronomy students, astrophysicists, and educators interested in celestial mechanics and gravitational calculations will benefit from this discussion.

Surgikill117
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Homework Statement



Table 5-2 gives the mean distance, period, and mass for the four largest moons of Jupiter (Those discovered by Galileo in 1609). A) Determine the mass of Jupiter using the data for Io B) Determine the mass of Jupiter using data for each of the other three moons. Are the results consistent?


Table
Moon Mass(kg) Period (Earth Days) Mean distance from Jupiter in km
Io 8.9*10^22 1.77 422*10^3
Europa 4.9 3.55 671
Ganymede 15 7.16 1070
Callisto 11 16.7 1883


Homework Equations



g1=G((m1m2)/r^2)
m1=(r^2*g1)/(Gm2)

The Attempt at a Solution



I don't know how to find g1 with the given information. Do I eliminate m2 in order to find g1? I also have no idea what the purpose of the period is, is it just there to confuse us?
 
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Try using Kepler's laws.
 

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