Knocking on Heaven's Door - Lisa Randall [167]
Objects in outer space have a large range of sizes as well. Asteroids, for example, vary quite a bit—tiny ones can be as small as pebbles, while bigger ones are far greater than any feature on Earth. At approximately a billion meters across, the Sun is about 100 times the size of the Earth. And the solar system, which I’ll take to be roughly the distance from the Sun to Pluto (which is in the solar system whether or not it merits planet status) is about 7,000 times the radius of the Sun.
The distance from the Earth to the Sun is considerably smaller—a mere 100 billion meters—a hundredth of a thousandth of a light-year. A light-year is the distance light can travel in a year—the product of 300 million meters/second (the speed of light) and 30 million seconds (the number of seconds in a year). Because of this finite speed of light, the illumination we see from the Sun is already about eight minutes old.
Many visible structures, of varying shapes and sizes, exist within our vast universe. Astronomers have organized most astral bodies according to type. To set some scales, galaxies are typically about 30,000 light-years or 3 × 1020 meters across. That includes our galaxy—the Milky Way—which is about three times that size. Galaxy clusters, which contain from tens to thousands of galaxies, are about 1023 meters in size, or 10 million light-years big. Light takes about 10 million years to traverse from one end of a galaxy cluster to the other.
Yet despite the huge range of sizes, most of these bodies act in accordance with Newton’s laws. The orbit of the Moon, like the orbit of Pluto, or the orbit of the Earth itself, can be explained in terms of Newtonian gravity. Based on the planet’s distances from the Sun, its orbit can be predicted with Newton’s gravitational force law. That’s the same law that caused Newton’s apple to fall to Earth.
Nonetheless, more precise measurements of planetary orbits revealed that Newton’s laws were not the final word. General relativity was needed to explain the precession of the perihelion of Mercury, which is the observed change in its orbit around the Sun over time. General relativity is a more comprehensive theory that includes Newton’s laws when densities are low and speeds are small, but also works outside these restrictions.
General relativity isn’t needed to describe most objects however. But its effects can accumulate over time, and are prominent when objects are sufficiently dense, as with black holes. The black hole at the center of our galaxy is about 10 trillion (1013) meters in radius. The enclosed mass is very large—about 4 million times the mass of the Sun—and, as with all other black holes, requires general relativity to describe its gravitational properties.
The entire visible universe is currently 100 billion light-years across—1027 meters, a million times the size of our galaxy. That is enormous and superficially surprising since it is bigger than the distance we can actually observe, 13.75 billion years since the time of the Big Bang. Nothing is supposed to travel faster than light speed so with the universe only 13.75 billion years old, this size might seem impossible.
However, no such contradiction exists. The reason the universe as a whole is bigger than the distance a signal could have traveled given its age is that space itself has expanded. General relativity plays a big role in understanding this phenomenon. Its equations tell us that the very fabric of space has expanded. We can observe places in the universe that are that far apart, even though they cannot see each other.
Given the finite speed of light and the finite age of the universe, this section has now taken us