What is the minimum speed needed for a cannonball to orbit the Earth?

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SUMMARY

The minimum speed required for a cannonball to achieve orbit around the Earth is determined by the principles of universal gravitation. When fired from the top of Mount Everest, the cannonball must reach a specific velocity to maintain a stable orbit without air resistance. The relevant equation for this calculation is Newton's law of universal gravitation, which describes the gravitational force between two masses. This discussion emphasizes the importance of understanding gravitational forces and orbital mechanics in achieving orbital velocity.

PREREQUISITES
  • Understanding of Newton's law of universal gravitation
  • Basic knowledge of orbital mechanics
  • Familiarity with the concept of escape velocity
  • Graphing skills to interpret Fg vs. r relationships
NEXT STEPS
  • Research the calculation of escape velocity for different celestial bodies
  • Learn about the effects of air resistance on projectile motion
  • Explore the relationship between gravitational force and distance from the Earth's center
  • Study the principles of orbital dynamics and satellite motion
USEFUL FOR

Physics students, aerospace engineers, and anyone interested in understanding the mechanics of orbital motion and gravitational forces.

saan100
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1) Graph Fg vs. r
Fg on y-axis, r on x-axis (from 1re to 6re)

re (radius of the Earth)

2) If a cannon ball is fired from the top of Everest parallel to the Earth's surface fast enough (ignoring air resistance and assuming that it doesn't bump into anything), it will "orbit" the Earth and hit the back of the cannon that it was fired from. Find the speed required to do this.
 
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