Indirect Measurements and Hubble's Constant

Date: 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/