Orbital Velocity Calculator
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README.md
orbital_velocity.py
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README.md

Orbital Velocity Calculator

These calculators calculate the orbital velocity of an object in a circular orbit around Earth at a given altitude above sea level.

The calculator estimates the velocity based on Newton's cannonball analogy, with a little help from Pythygoras's theorem and the constant linear acceleration formula.

The calculator also calculates the precise orbital velocity using orbital mechanics, and calculates the variance between the precise orbital velocity and the estimate.

Assumptions:

  • No air resistance at any altitude.
  • Earth is a perfect sphere.
  • Earth's gravity and acceleration due to gravity is uniform.
  • The object has negligible mass compared the Earth's mass.

Newton's Cannonball Thought Experiment

Imagine a cannonball being fired out of a cannon. It should travel in a straight line, if not for acceleration due to gravity.

Gravity will cause the cannonball to fall towards Earth at a constant rate of acceleration.

When the cannon is fired at normal velocity, the cannonball will fall to the ground at some distance from the cannon.

When the cannon is fired at a higher velocity, the cannonball fly even further before falling to the ground.

At orbital velocity, the cannonball will be falling as quickly as the surface of Earth is curving away from the cannonball.

How This Model Estimates Orbital Velocity

This model estimates the orbital velocity by calculating how long it takes for the cannonball to drop an arbitrary distance of 1km.

In the time it takes for the cannonball to drop that distance, the cannonball will have to had travelled such a distance that the Earth curves away from it by the same arbitrary distance of 1km.

The orbital velocity can be calculated by dividing that horizontal distance by the time it must have taken to cover that distance.

A more detailed walk-through can be found on my blog post: http://www.enochko.com/blog/newtons-cannonball-and-orbital-velocity