How Do You Calculate the Gravitational Acceleration of a Satellite in Orbit?

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SUMMARY

The gravitational acceleration of a satellite in orbit can be calculated using the formula g = GMe / r^2, where G is the gravitational constant (6.673 x 10^-11 N(m/kg)^2), Me is the mass of the Earth (5.9742 x 10^24 kg), and r is the distance from the center of the Earth to the satellite. For a satellite 3.59 x 10^7 m above the Earth's surface, the total radius r is the sum of the Earth's radius (approximately 6.371 x 10^6 m) and the height of the satellite. The correct calculation involves ensuring that the total radius is accurately used in the formula to determine the correct gravitational acceleration.

PREREQUISITES
  • Understanding of gravitational force and acceleration
  • Familiarity with the gravitational constant (G)
  • Knowledge of Earth's mass (Me) and radius (Re)
  • Ability to manipulate equations involving exponents
NEXT STEPS
  • Calculate the total radius r by adding Earth's radius to the satellite's height
  • Revisit the gravitational acceleration formula g = GMe / r^2 with correct values
  • Explore the implications of altitude on gravitational force
  • Study the effects of orbital mechanics on satellite positioning
USEFUL FOR

Students in physics or engineering courses, educators teaching gravitational concepts, and anyone interested in satellite dynamics and orbital mechanics.

Meroko
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Homework Statement


Synchronous communications satellites are placed in a circular orbit that is 3.59 X 10^7m above the surface of the earth. What is the magnitude of the acceleration due to gravity at this distance?


Homework Equations


F=G M1M2 / R^2/ mp
g= GMe / r^2
r= Re + H
w=mg
g=w/m

The Attempt at a Solution


I tried to put the numbers in the "g= GMe / r^2" equation, which turns out to be
g= 6.673 X 10^-11 X 5.9742 X 10^24 /( 3.59 X 10^7)^2

But the answer that I got is wrong. Can someone please help me fix my mistakes and help me get the right answer?
 
Physics news on Phys.org
Consider the third equation in your list of relevant equations.
 

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