How Do Spacecraft Velocities Change in Different Orbits?

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SUMMARY

The discussion focuses on calculating the velocity of a spacecraft in different orbital scenarios, specifically an elliptical orbit and a circular orbit. The spacecraft, with a mass of 1000 kg, is initially at a distance of 1.2 x 107 meters from the Earth's center, moving at a velocity of 7.1 x 103 m/s. Key calculations include the mechanical energy of 8.1 x 109 J and angular momentum of 8.52 x 1013. The minimum escape velocity from Earth is also discussed, emphasizing the need for understanding gravitational forces and orbital mechanics.

PREREQUISITES
  • Understanding of gravitational forces and orbital mechanics
  • Familiarity with the concepts of mechanical energy and angular momentum
  • Knowledge of escape velocity calculations
  • Basic proficiency in physics equations related to motion and orbits
NEXT STEPS
  • Research the concept of escape velocity and its derivation
  • Learn about the differences between elliptical and circular orbits in celestial mechanics
  • Explore the implications of angular momentum conservation in orbital dynamics
  • Study the effects of mass and distance on gravitational force
USEFUL FOR

This discussion is beneficial for physics students, aerospace engineers, and anyone interested in understanding spacecraft dynamics and orbital mechanics.

Kelseywelsey
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Homework Statement


A spacecraft of mass 1000 kg is in an elliptical orbit about the earth. At point A the spacecraft is at a distance of 1.2 x 10^7 meters form the center of the Earth and its velocity ( 7.1 x 10^3 m/s) is perpendicular to the line connecting the center of the Earth to the spacecraft . Mass of the earth= 6.0 x 10^24 and radius= 6.4 x 10^4. I need to find the speed of the spacecraft if it is in a CIRCULAR orbit and the minimum speed of the craft at pt. A if it is to escape completely from the earth.


Homework Equations



V at point B= 2400 m/s

The Attempt at a Solution



So far, I've figured that the mechanical energy is 8.1 x 10^9 J
Angular momentum= 8.52 x 10^13
and speed at a point directly across from A
V= 2.4 x 10^3
 
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Alright, so more than just telling us what numbers you have, you should go over some concepts and why you chose these numbers.

What kind of questions do you have that could be answered and potentially helpful to you solving the problem?

More importantly, what is it that is keeping the spacecraft in orbit? How do you think that case will be broken?
 

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