Indirect Measurements and Hubble's ConstantDate: 01/31/2003 at 12:46:56 From: Dan Subject: Indirect Measurements How are indirect measurements used in astronomy? For example, how can scientists tell how far the Earth is from Pluto? Date: 02/01/2003 at 21:35:17 From: Doctor Edwin Subject: Re: Indirect Measurements Hi, Dan. There are a number of ways scientists can determine distances in astronomy. Within the solar system, you can use orbital period. The orbital period of a planet varies as the square root of the cube of the distance from the sun: T = k * r^(3/2) where T is the time for one revolution, r is the distance between the centers of the Sun and the planet, and k is a constant. So if you know how much longer it takes another object to go around the Sun than it takes the Earth, we can know how many times farther away it is. Another method is parallax. Here's a diagram: * -- star /|\ / | \ / | \ / |b \c / | \ / | a \ Earth in January o------O------o Earth in July Sun You measure the position of a star in the sky, and then again 6 months later when the Earth is on the opposite side of its orbit. If you know the distance a, and you measure the angle ac, you can figure out using trigonometry how long c is (a / cos(ac)). This only works for objects within a few dozen light-years of Earth. Objects farther away don't change their position in the sky enough as the Earth swings from one side of the sun to the other. Farther than that and we must rely on measurements that make some assumptions. For example, we might assume that the biggest stars in a galaxy like ours are about as bright as the brightest stars in our own galaxy. If we know about how bright they must be, and we know how bright they look to us, then we can guess how far away they must be. Another indirect measurement of distance is the red-shift. Light coming from objects that are moving away from us is redder than light from stationary objects. This is due to the Doppler effect, and you should be able to find lots of references to it. Now when scientists first started measuring the light from stars, they noticed that some were redder than they should be. Someone named Hubble figured out that meant they must be moving away from us. By comparing with other measurements of distance, he figured out that there was a straightforward relation. The farther something was from us, the faster it was moving away from us. This meant that the universe was expanding. Now it is very hard to pin down a good number for what we now call Hubble's Constant. So if we guess the distance to a faraway galaxy by using its red-shift, we can only know approximately how far away it is. Hope this helps. Write back if you need more info. - Doctor Edwin, The Math Forum http://mathforum.org/dr.math/ |
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