M is also different. After all, you don't care about the part of the shell above the object.anhchangdeptra said:Oh! So we only care about the smaller shell with radius= R/2. The distance from mass m to the center is r so basically we have the same formula as for an object outside the bigger shell= (GMm)/r^2 (only the r is different is the two cases)?
The Shell Theorem is a mathematical principle that states that the gravitational force exerted by a spherically symmetric mass distribution on a particle located outside of the distribution is the same as if all of the mass were concentrated at the center of the sphere.
The Shell Theorem is significant because it simplifies the calculation of gravitational forces in many situations, particularly in celestial mechanics. It also helps to understand the behavior of planetary orbits and the structure of stars and galaxies.
The Shell Theorem can be applied in various real-life situations, such as calculating the gravitational force between planets and stars, understanding the behavior of satellites in orbit, and predicting the structure of celestial bodies such as galaxies.
The Shell Theorem is based on several assumptions, such as the spherical symmetry of the mass distribution and the fact that the particle is located outside of the distribution. These limitations may not apply in all situations, and therefore the Shell Theorem may not accurately predict gravitational forces in certain scenarios.
The Shell Theorem was first derived by Sir Isaac Newton in his famous work, "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy), published in 1687. However, it was later refined and expanded upon by other scientists, such as Pierre-Simon Laplace and Joseph-Louis Lagrange.