Newton’s triumph was that he could use his rules to explain why the planets moved in ellipses, and thus derived Kepler’s laws of planetary motion from physical principles. But one thing Newton couldn’t do was determine the value of his gravitational constant, known as G. The only gravitational forces he could observe were between the planets Moon and Sun, and no one had any idea what their masses were. Without them, the value of G couldn’t be determined.
Gravity Check
Yesterday I wrote about how we test whether unitless constants such as alpha (α) change over the history of the universe. You might also have noticed that I said if such constants did change, then it would mean either fundamental physical constants change or there is some exotic physics going on. We looked at the physical constants yesterday, so today let’s look for exotic physics.
Point of No Return
If you toss a ball up into the air, it will fall back to the ground. Toss one faster, and the ball will travel higher before returning to the ground. Of course this raises the question of just how fast you would have to throw a ball for it to never fall back down. Put another way, could you throw …
In the Red
If you toss a ball into the air, it will slow down as it rises. The Earth’s gravity pulls on the ball as it moves upward, causing it to slow down until it comes to a momentary stop at its highest point. Then it will begin to move downward, speeding up as it does. Suppose, then, that you were to shine a flashlight upward. What would happen? You might argue that gravity would pull on the photons, causing them to slow down, but we know that light has a constant speed, and can’t slow down. You might argue that since photons are massless gravity doesn’t affect them, but we know that the Earth’s mass, like any other mass, can cause light to change directions. So neither of these can be the answer. The real answer is pretty interesting, and it turns out to be one of the tests of Einstein’s theory of relativity.
If It Ain’t Got That Swing
A pendulum is a remarkably simple device that can be used in a range of scientific experiments. It can be used to measure the Earth’s rotation, for example. It can also be used as a timing mechanism. The period at which a pendulum swings depends upon the distribution of mass throughout the pendulum (known as the moment of inertia) and the distance of the swing point from its balance point (center of mass). The period also depends upon the acceleration of gravity, known as g. Because of that you can also use a pendulum to measure Earth’s gravity.
Secular and Periodic
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.
Spirals
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.
Bend It Like Newton
Yesterday’s post on testing the assumption that photons are massless raised a few questions for readers. One of the most common was the idea that the gravitational lensing of light must mean that photons have mass. After all, if a star or galaxy can deflect light gravitationally, doesn’t that mean the light is gravitationally attracted to it? If that is the case, doesn’t that mean that light has mass?
By the Numbers
The orbits of three of the moons of Jupiter (Io, Europa and Ganymede) have an interesting pattern. For every time Ganymede orbits Jupiter, Europa orbits twice, and Io orbits four times. In other words, the periods of their orbits follow the ratio of 1:2:4. This is known as an orbital resonance, and it occurs a number of times in our solar system. Saturn’s moons of Hyperion and Titan have a 3:4 resonance, and Pluto and Neptune a 2:3.