 If we scale up our previous earthbound bullet example to galaxies in the universe, we can apply Newton's equations for force, gravity, acceleration, and his shell theorem to gauge how the universe might evolve over time. Picture a wide enough expanse of the universe so that the cosmological principle holds true. We'll center our example on ourselves here in the Milky Way. We are at rest in our own reference frame. Consider a galaxy like IC-1101 a billion light years away. Our question comes down to how will this galaxy move with respect to us? Given the galaxies are made up of electrically neutral molecules, the only force at work here is gravity. If we build a sphere with us at the center and IC-1101 at the surface, we can calculate the gravitational force on an acceleration of IC-1101 from all the matter, from all the galaxies within the sphere. And we can use Newton's shell theorem to cancel out all the other gravitational forces in the universe. We find that the mass density inside the sphere is all that matters. If we take a look at this equation for a minute, you can see its implications for cosmology. If the acceleration, r double dot, is zero, then the mass density of the universe, rho, would have to be zero. In other words, the universe cannot be static unless it's empty. The existence of matter in the universe means that galaxies must not only be moving, they must be accelerating. The other thing to note is that the acceleration is always negative, meaning that it is in the direction of contraction. But we know from our examination of escape velocity that initial conditions can have the universe expanding, even as that expansion is slowing down. Looking at it from an energy point of view, Alexander Friedman, a Russian mathematician and physicist using Newton's model, developed an equation now named after him which showed how the universe would behave under various initial conditions. The constant u in the equation represents the total energy per unit mass at the surface of the expanding sphere. There are three possibilities for this constant. It will be zero if the kinetic energy is equal to the gravitational binding energy. In this case, an early rapid expansion will continue to slow as it approaches a steady volume, but never reaches it. This is like the bullet example having the exact escape velocity. It will be a positive number if the kinetic energy is large enough to overcome the gravitational binding energy. In this case, the universe will expand forever. This is like the bullet examples having exceeded the escape velocity. And it will be a negative number if the kinetic energy is insufficient to overcome the gravitational binding energy. In this case, the universe will eventually collapse. This is like the bullet examples having less than the escape velocity. Note that r dot over r is velocity over distance. This is the Hubble constant. We see that it can vary with time. This means that the Hubble constant is not really constant. We call it the Hubble parameter. The value we've been measuring is designated H naught and represents the value of the Hubble parameter at the current time.