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Now, invoking Bertrand's theorem with regard to the Kepler problem of the motion of a body in a central force, one can show that the only cases for which closed orbits are stable are that of the inverse square law and Hooke's law for the force. I find it kind of remarkable that the requirement of stability of closed orbits is sufficient to constrain the form of the central force to just two cases.
If you assume gravitational flux[1] is conserved, then flux density, and thus force at a given point, must decrease proportional to the increase in surface area over which it distributed. Thus, inverse-square. As for why it's a nice even number, it's because we live in a universe with a nice integral number of dimensions.
The gravitational force between two masses outside a uniform field is defined by Newton’s Law of Gravitation. Although planets are not point masses, their separation is much larger than their radius. Therefore, Newton’s law of gravitation applies to planets orbiting the Sun. The 1/r 2 relation is called the ‘inverse square law’.
Aug 6, 2024 · That leads to a force law where gravity gets weaker in precisely the same way: as though it’s proportional to ~1/r². The reason gravity follows a ~1/r² force law is because we live in a ...
- Ethan Siegel
Since the force of gravity does lie along the line joining the two particles, we can cheat a bit and treat this as a one-dimensional problem, with \((F^G _{12})_x = −Gm_1m_2/(x_1 − x_2)^2\) (I’ve put a minus sign there under the assumption that particle 1 is to the left of particle 2, that is, \(x_1 < x_2\), and the force on 2 is to the left), and find a potential energy function whose ...
Most who study physics knows Newton's famous equation for the force of gravity between two objects is an inverse-square law: F = GMm/r^2. But the question c...
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- Doc V Physics
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Sep 25, 2024 · In Newton’s equation F12 is the magnitude of the gravitational force acting between masses M1 and M2 separated by distance r12. The force equals the product of these masses and of G, a universal constant, divided by the square of the distance. The constant G is a quantity with the physical dimensions (length) 3 / (mass) (time) 2; its ...
