How Much Force Keeps a Satellite in Orbit at Three Earth Radii?

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SUMMARY

The force of gravity acting on a 4500 kg satellite orbiting three Earth radii from the Earth's center is calculated using the formula Gm1m2/r². Given the mass of the Earth as 5.98 x 10^24 kg and the radius of the Earth as 6370 km, the correct calculation requires converting the radius to meters. The final answer, after proper unit conversion, aligns with the multiple-choice options provided, specifically 5000 N.

PREREQUISITES
  • Understanding of gravitational force calculations using Newton's law of universal gravitation.
  • Familiarity with unit conversions, particularly between kilometers and meters.
  • Basic knowledge of physics concepts related to satellite motion and orbits.
  • Proficiency in using scientific notation for large numbers.
NEXT STEPS
  • Study the derivation and application of Newton's law of universal gravitation.
  • Learn about satellite dynamics and the factors affecting orbital stability.
  • Explore unit conversion techniques, especially in physics contexts.
  • Investigate the implications of gravitational force variations at different altitudes.
USEFUL FOR

Students in physics, aerospace engineers, and anyone interested in understanding satellite mechanics and gravitational forces.

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Homework Statement


What is the force of gravity acting on a 4500kg satellite when it orbits three Earth radii from the Earth's center?

Homework Equations


Gm1m2/r²
mass of the earth=5.98*10^24kg
radius of the earth=6370km

The Attempt at a Solution


This is a multiple choice question, with answers:
15000N
45000N
500N
1500N
5000N

However, what I get from plugging in is:
[(6.67*10^-11)(4500)(5.98*10^24)]/(3*6370)²
which equals roughly: 5.0*10^9 which is completely off any of the answers... can anyone help me?

hahaha, never mind! I forgot to convert the km to m... -_-
 
Last edited:
Physics news on Phys.org
You're not using SI units for distance.
 

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