Tag Archives: gravity
From the Equivalence Principle to Curved Geometry of Spacetime
Newtonian mechanics contains two masses with no obvious reason to be related. One appears in the law of gravitation, $$\mathbf{F}=-\frac{GMm_g}{r^{2}}\hat{\mathbf r},$$ where $m_g$ measures how strongly a body couples to a gravitational field. The other appears in the second law, … Continue reading
Posted in Expository, Notes
Tagged Classical Gravity, curvature, differential geometry, Einstein equations, equivalence principle, general relativity, geodesic deviation, Geodesics, gravity, Lorentzian Geometry, manifolds, Mathematical Physics, spacetime, Tensors, theoretical physics
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How a Molecular Cloud Collapses Into a Star
Making a star means compressing gas by something like twenty-four orders of magnitude. The warm neutral interstellar medium, the ordinary atomic gas between the stars, holds roughly a third of a hydrogen atom per cubic centimetre at a temperature of … Continue reading
The rubber sheet gets the geometry right and the mechanism wrong!
You have seen this demonstration. Somebody stretches a rubber sheet over a frame, drops a bowling ball in the middle, and the sheet sags. Then they roll a marble across it and the marble curves toward the bowling ball, maybe … Continue reading
Posted in Diary, Expository, Notes, Scratch essays
Tagged Astrophysics, debunking, equivalence principle, general relativity, Geodesics, gravitational waves, gravity, manifolds, Mathematical Physics, philosophy of science, physics, Schwarzschild metric, science, science writing, spacetime, spacetime curvature, theoretical physics
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Deriving the Euler–Lagrange Equation for Particles, Fields, and Curved Spacetime
A good way to understand the laws of motion is not to memorize a separate equation for each situation, but to notice there is really only one trick, and every equation of motion is what falls out when you apply … Continue reading