Artificial satellite velocity (around the earth)

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SUMMARY

The velocity of an artificial satellite orbiting the Earth can be calculated using the formula v = √(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the radius from the center of the Earth to the satellite. This equation indicates that the orbital velocity is directly related to the radius and the acceleration due to gravity, which is expressed as GM/r². While it is possible to determine the satellite's velocity using only the radius and local gravitational acceleration, incorporating the mass of the Earth yields a more precise calculation due to variations in gravitational force at different distances.

PREREQUISITES
  • Understanding of gravitational constant (G)
  • Familiarity with the mass of the Earth (M)
  • Knowledge of centripetal acceleration
  • Basic algebra for solving equations
NEXT STEPS
  • Study the gravitational constant (G) and its significance in orbital mechanics
  • Explore the relationship between radius and gravitational acceleration in satellite motion
  • Learn about variations in gravitational force at different altitudes
  • Investigate advanced orbital mechanics concepts, such as Kepler's laws of planetary motion
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in satellite dynamics and orbital mechanics will benefit from this discussion.

bullroar_86
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I know how to find the the velocity if I can use the mass of the earth.

Is it possible to find it with just the radius and acceleration?
 
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If you've already calculated the local force of gravity, then you just need to solve the centripetal acceleration equation for velocity.
 


Yes, it is possible to find the velocity of an artificial satellite around the Earth using just the radius and acceleration. The equation for the orbital velocity of a satellite is v = √(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the distance between the satellite and the center of the Earth (radius). This equation shows that the velocity of a satellite is dependent on the radius and acceleration due to gravity (GM/r^2). So, if you know the radius and the acceleration due to gravity at that distance, you can calculate the velocity of the satellite. However, knowing the mass of the Earth can provide a more accurate calculation as it takes into account the varying gravitational force at different distances from the Earth's center.
 

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