High school Circular Motion Help?

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SUMMARY

The discussion centers on solving a physics problem involving circular motion and gravitational forces related to Jupiter's moons, Ganymede and Callisto. The user correctly identifies Callisto as the slower moon based on its semi-major axis and mass. To calculate the necessary thrust for the spacecraft, the user needs to apply Newton's second law and consider the gravitational pull using the formula F=GMm/r^2. Additionally, understanding orbital speeds and their relationship to mass is crucial for further analysis.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with gravitational force calculations using F=GMm/r^2
  • Knowledge of orbital mechanics and semi-major axes
  • Basic concepts of thrust and acceleration in spacecraft dynamics
NEXT STEPS
  • Study Newton's second law and its application in spacecraft dynamics
  • Learn about gravitational interactions and orbital mechanics
  • Research the specific orbital speeds of celestial bodies in the solar system
  • Explore the relationship between mass and orbital period for planets and moons
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and gravitational forces, as well as educators looking for practical examples of circular motion in celestial contexts.

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Homework Statement


Part 1
You are traveling to Jupiter's moons:Ganymede and Callisto. You have to land on the slower moon before trying to accelerate to the faster moon. Which moon will you land on first? What must your velocity be in order to "catch up"(accelerate) to the faster moon?

Part 2
Your spacecraft weights 2.04x10^6kg and the fluid friction from the slow moom is 500,000N. The Acceleration due to gravity is 1.3m/s^2. If it takes 30 mins to accelerate to the faster moon, how much thrust does the spacecraft exert?

Homework Equations


G=6.67x10^-11m^3/kg^2
Ganymede: Mass=1.48x10^23kg, Semi-Major Axis=1,070,400km
Callisto: Mass=1.076x10^23kg, Semi-Major Axis=1,882,700km

The Attempt at a Solution


I used F=GMm/r^2 to find the pull between the two moons and Jupiter, and I think that the slower moon would be Callisto. But I don't think that's the right equation to use. And now I have no idea where to even start the other parts of the question.I really want to understand because I don't really get my teacher's explanation. So any help would be greatly appreciated.
 
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Think about this, what are the orbital speeds of the planets in the solar system? Is there some kind of relationship? Would the relationship, if it exists, be the same for juipters moons?

Now what about two planets the same distance from the sun, one with twice the mass as the other. Which planet would orbit quicker?
 

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