 We'll now turn our attention to the kinds of massive accelerating objects that can create such a wave. In order to generate a gravitational wave, you need a non-spherically symmetric rotating system. For example, here's a binary star system with two masses revolving in a circular orbit around a common center of gravity. The star's acceleration creates gravitational radiation that travels out from the system in all directions, just like the light they are generating. The gravitational wave solutions show that the frequency of the created gravitational wave is twice the rotation rate of the binary system. We also see that the polarization and maximum gravitational wave amplitude depend on the masses of the two objects, the distance between them, their rotation of velocity, the viewing angle, and how far away the system is from the observer. There is one more key factor to consider when it comes to binary systems, namely that the gravitational waves carry energy and momentum away from the system. We call this gravitational luminosity. Newton and Kepler provided the mechanics for understanding what happens to the orbit when gravitational energy is lost. Because binding energy is negative, a loss of energy will make it a larger negative. This has the effect of reducing the distance between the two objects. This in turn increases their velocity. A shorter circumference and faster velocity reduces the time it takes for a full orbit and therefore increases the frequency of rotation and therefore the frequency of the gravitational wave. And the wave equations show that the amplitude of the gravitational wave will increase with the frequency. The rate that the frequency is changing is called the chirp. It gives us the ability to express the amplitude of the gravitational wave in terms of the frequency and the rate the frequency is changing. This is crucial, because for most cases we will have no way of knowing directly what the masses are or how far apart they are, but measuring the frequencies might be possible. If we can also measure the amplitude, we can even calculate the distance to the binary system. Because this distance is based on gravitational wave luminosity, it is called the luminosity distance. For most all gravitational wave sources, this will be the only way to figure out how far away they are. With a decaying orbit, the objects will eventually collide and coalesce. The resulting wave form, called a coalescing wave form, serves as a signature for this kind of gravitational wave source. It has three phases, the inspiral, the merger, and the ring down to an object that is no longer asymmetric and therefore no longer radiating gravitational waves. To get an idea on the expected amplitudes and frequencies for gravitational waves created by a system like this one, let's put in some numbers. Because this system is 100 light years away and each star is the mass and size of our sun, at the point where they are about to touch, we would see the maximum amplitude. In this example, we get 10 to the minus 21. This is a very small number. It is approximately the ratio of the width of a human hair to the distance to Alpha Centauri, 4 light years away. Here is where this data point fits on a graph with wavelength decreasing along the x-axis and amplitude increasing along the y-axis. Binary systems like this one are plentiful and all around us. There are literally billions of them sending gravitational waves our way from every direction. But the gravitational waves they create are weak and totally indistinguishable from one another. They just wind up contributing to a background noise level. In our sensitivity graph, we see that in order to detect a gravitational wave, a binary system will have to create waves with greater amplitudes and higher frequencies to generate smaller wavelengths than the noise level marked in green. To stand out, a binary system is needed that can achieve much higher velocities. And as we have seen from our example, the large diameters of stars prevents them from ever getting close enough to reach the needed velocities.