Abstract
In his monumental Principia, Newton formulated the general laws of motion and the law of universal gravitation. He then applied these laws to explain the motion of planets and comets, projectile trajectories, and the marine tides, among other things.
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- 1.
Even a motionless puck on frictionless ice is subject to forces. Gravity pulls the puck downwards, but the surface of the ice pushes back with equal and opposite force, so the total force on the puck is zero.
- 2.
The law of inertia was actually discovered by Galileo and was adopted by Newton as one of his laws of motion.
- 3.
Newton also formulated a third law, which states that in every interaction between two bodies, the force the first body exerts on the second body is equal and opposite to the force the second body exerts on the first. If you push your friend facing you on an ice-rink, she will coast backwards, but so will you.
- 4.
The Earth is not exactly an inertial frame because of its rotation about its axis, which can be observed with a Foucault pendulum.
- 5.
To prove the shell theorem, Newton represented the shell as consisting of a large number of point masses and added together the forces produced by all of these masses. He had to invent calculus to perform this calculation!
- 6.
The derivation of this formula relies on some simple geometry and can be found in any basic physics textbook.
- 7.
This formula can also be used for a small object (like a human) interacting with a large spherical body (like the Earth). In this case, the small object does not have to be spherical, and the distance r is the distance from any point in the object to the Earth’s center.
- 8.
You probably remember what happens when you are pulled up and released on a swing: you start from rest, reach a maximum speed at the bottom of your trajectory and then slow down as you swing up, momentarily coming to rest before going backwards, and so on.
- 9.
Note that the final energy is purely kinetic and must therefore be positive. This says that only objects with positive (or zero in the marginal case) total energy can escape.
- 10.
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Perlov, D., Vilenkin, A. (2017). Newton’s Universe. In: Cosmology for the Curious. Springer, Cham. https://doi.org/10.1007/978-3-319-57040-2_2
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DOI: https://doi.org/10.1007/978-3-319-57040-2_2
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