More general relativity today. This time a bit on how to calculate the perihelion advance of Mercury in general relativity. When you derive the central force equation for relativistic gravity you find there is an extra term not seen in Newton’s gravity. The extra term is small, but enough to make Mercury’s orbit (any orbit really, but we typically use Mercury as an example) deviate slightly from an ellipse. Since the deviation is small, you can make some broad approximations, get an approximate solution for Mercury’s orbit, then determine the perihelion advance for one orbit.
A while back I wrote about how general relativity predicts gravitational waves. While we haven’t yet observed gravity waves directly, we know they exist. That’s because gravitational waves carry energy away from their source, just as light waves carry light energy.
One aspect of general relativity that always amazes me is the level of precision needed to distinguish it from Newtonian gravity. Take, for example, the advance of Mercury’s perihelion. When you count in the gravitational tugs from the sun and all the planets, Newton predicts Mercury’s perihelion will advance about 531.65 arcseconds per century. When we measure the orbit of …
Newton’s laws of motion and gravity predicted the motions of the planets almost perfectly. Newton’s laws are so accurate that we use them to accurately send robotic probes to Mars and other planets, but Newton’s laws aren’t perfect. The motion of some planets differ very slightly from Newton’s predictions. In the case of Uranus, its small deviation led to the discovery of Neptune. In the case of Mercury, however, its small deviation led to a completely new understanding of gravity.
One of the predictions of general relativity is that the motion of large masses, such as a binary system of black holes or neutron stars, should produce gravitational waves. When most people think of waves they typically think of water waves. Drop a pebble in a calm pond and you can watch the waves spread out over the surface of …
From the photon’s perspective, the instant it is emitted in the Andromeda galaxy, it strikes your eye.
There’s been a couple of questions about the possibility of traveling faster than light, so let’s explore that a bit today. The short answer to whether one can travel faster than light is no. The inertial speed of an object can never exceed the speed of light. This means if you measure the speed of an object passing you, it will always be less than the speed of light. The longer answer is “it’s complicated.”
It turns out that the rotation of a mass also distorts space and time. For example, as the Earth rotates, it drags the nearby space along with it (an effect known as frame dragging). Similar to water spiraling down a drain, this effect builds up, and as a result, space spirals a bit around the Earth. You have to be a bit careful with this comparison. Spacetime doesn’t “flow” the way water does, but the spiral effect is somewhat similar.
After the Michelson-Morley experiment, several theorists tried to explain the results by supposing that Earth dragged the aether along with it, or imposed other conditions to explain our inability to observe the aether. But then Einstein proposed special relativity, which eliminated the need for aether altogether.