Newton's Cannon - Speed vs Height

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Rocket V 7 km/s Rocket Dist 6380kmkm
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Newton came up with the Cannon thought experiment to demonstrate to people of his era how orbits can arise from the force of gravity. Using the simulation of Newton's canon we can see another important propoerty of orbits, and that is what happens if we extend the mountain upwards. You may have noticed that the cannon ball had to reach a velocity of over 7100 meters/second to orbit the earth. This is the starting condition in the scenario in this simulation as well. The starting conditions are identical, and if you simply hit the Run button you will see the orbit from the previous simulation. However, there is now a slider for the Satellite Distance--the distance of the cannon ball/satellite from the centre of the planet and a slider for the speed.

Try varying the distance slider and speed slider to find the speed you need to achieve circular orbits for different heights.

You will find that the higher the starting point, the slower the starting speed needed to orbit the planet. You can also see that given that a circular orbit at a larger distance from the planet traces out a larger circumference the satellite takes longer to orbit the planet. Higher orbits are slower and longer.