# Gravity Check

19 April 2014

Newton’s law of gravity states that between any two masses there is a gravitational force. The strength of that force depends not only on the masses, but on the distance between those masses, following what is known as an inverse square relation. That is, if you double the distance between two masses, their gravitational attraction will be a quarter of what it was. If you halve the distance between two masses, their attraction will be four times stronger. Newton felt that this inverse square relation was exact, but is it?

One of the ways we know Newton’s gravity works is through the motion of the planets. Masses like the planets and Sun are attracted to each other by gravity’s inverse square relation, and thus their motion follows a relation known as Kepler’s laws. We have seen that this holds not only for the planets and moons in our solar system, but also for other stars orbiting each other, exoplanets orbiting their star, and even stars orbiting the supermassive black hole in the center of our galaxy. So Newtonian gravity works very, very well.

For large masses we know that the inverse square relation for gravity isn’t quite exact. For example, Mercury and the Sun are massive enough and close enough that Mercury’s orbit deviates slightly from a simple elliptical orbit. This deviation was the first evidence of general relativity. We also know that the orbit of massive neutron star orbiting with another star will decay in a way that violates Newtonian gravity (but agrees with general relativity). Newtonian gravity works very well, but for massive objects general relativity is more accurate.

What about for small masses on very short scales?

We know that on very small scales Newtonian physics is inaccurate, and we need to use quantum mechanics. One common feature of quantum mechanics is that rather than being smooth and continuous, objects can be constrained into discrete (quantum) states. We see this, for example, in the light emitted by an atom. Rather than being a continuous range of wavelengths, the emitted light can only be at particular wavelengths. This is due to the fact that an electron in an atom can only have particular energy levels. When an electron drops from a higher energy level to a lower one, it releases a photon of a particular wavelength.