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### 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.

- Doctor Edwin, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Practical Geometry
Middle School Geometry
Middle School Measurement

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