How Do Orbital Dynamics Affect Satellites with Different Masses and Distances?

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Homework Help Overview

The problem involves three satellites orbiting a planet, with varying masses and distances from the planet's center. The original poster seeks to determine the orbital periods and gravitational forces acting on the satellites based on their respective distances and masses.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions whether to consider the gravitational interactions between the satellites and seeks guidance on how to approach the problem. Some participants explore the implications of Kepler's third law for determining orbital periods, while others discuss the calculation of gravitational forces based on mass and distance.

Discussion Status

Participants are actively engaging with the problem, offering various interpretations and reasoning. Some have proposed potential relationships between the periods of the satellites, while others are calculating forces based on gravitational equations. There is no explicit consensus yet, but multiple lines of reasoning are being explored.

Contextual Notes

The original poster has provided specific values for the forces and periods of one satellite, which may influence the calculations for the others. There is uncertainty regarding the necessity of considering inter-satellite forces.

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Homework Statement


Three satellites orbit a planet of radius R. Satellites s1 and s3 have mass m. Satellite s2 has a mass of 2m. Satellites s1 & s2 have orbits 2R from the center of the planet. Satellite s3 has an orbit of 3R from the center of the planet. Satellite s1 orbits in 250 minutes and the force on s1 is 10,000 N

a)What are the periods of s2 and s3?
b)What are the forces on s2 and s3

Homework Equations


T= [(4pi)^2/GM]*r^3


The Attempt at a Solution



As I'm starting this problem, I'm wondering: Do I have to consider the forces between the satellites as well? And if I do, how will I know the distances between them? Or is the force on s1 only the force from the gravity of the planet? Can I get some suggestions on how to start this?
 
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Is this going to end up being an expression or a number?
 
Ok, I just had some thoughts, according to Kepler's third law it seems to me that satellite 2 would also have a period of 250 minutes. Then by reasoning, increasing the radius by a factor of 1.5 would increase the period by a factor of 1.5^3 so the period of s3 would be 250* (1.5)^3. Is this correct?
 
F= GMm/r^2 So Then likewise, the force on s2 would be 20,000N & s3 would be 10000/(1.5^2)
 

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