Distance measurement in Astronomy
The measurement of distance is
crucial to our understanding of the scale of the Universe.
Radar
The distance from the Earth of objects in the Solar System can be measured using radar. A pulse
is sent out and the time taken for the reflected pulse to be received is recorded. Knowing the
speed of electromagnetic radiation in free space and the time between transmission and
reception the radar pulse enables us to find the distance of the object. For example the
elapsed time would be 2.5 s for the Moon and up to 50 minutes for Jupiter and around five
and a half hours for Pluto. (The last two numbers depend on the relative positions of the
Earth, Jupiter and Pluto in their orbits)
Parallax
The difference in direction of a star viewed from the two ends of a line with a length equal to the radius of the
Earth's orbit is called the PARALLAX of the star.
Stars that are close to the earth
clearly have a larger parallax than ones far away. In other words their direction when viewed
from the Earth changes significantly as the Earth orbits the Sun.
By significantly we mean a fraction
of a second of arc. In the example shown
a Centauri (distance 1.33 parsecs) has a parallax
of 0.75 " of arc.
Astronomical unit
One Astronomical unit (AU) is defined as the mean distance of the Earth from the Sun (1.5x10
11
m)
The light year
This is the distance that light travels in free space in
one year = 9.5x10
15 m
The Parsec
The radius of Earth's orbit =
1.5x10
11 m, and therefore the distance is found from:
tan(1") = 1.5x10
11/d so d = 3.06 x10
16 m
Distances between galaxies are usually measured in light
years or Mega parsecs (Mpc).
The parallax of a number of
stars is shown in the following table.
At distances much greater than this the parallax method
becomes impossibly difficult to measure. Remember that 1" of arc is the angle subtended by
a human head almost ¾ of a kilometer away. Therefore the parallax of Castor is the same as
the angle subtended by a human head at a distance of almost 750 km!
Another
method for measuring larger distances had to be found.
Cepheid variables
The solution came early in the twentieth century as a result of studies of
a variable star (one whose brightness changes with time) in the constellation of Cepheus.
The brightness of the star varied in a
particular way (see Figure 3) and in 1912 Miss Henrietta Leavitt of Harvard College
observatory discovered an important connection between the period and brightness. This is
now known as the period-luminosity relationship. Many other stars were found to vary in a
similar way and the group of stars was called Cepheid variables. (There are actually two
types of Cepheid variable but we will just consider one type here).
The period-
luminosity relation means that if you can measure the period of a Cepheid variable you can
find its luminosity. Knowing how bright the star really is and then measuring how bright it
appears to be will then give the distance of the star from the Earth. The discovery of Cepheid
variables in the Andromeda nebula (M31) enabled its distance from Earth (over two million
light years) to be found.
Two ways of presenting the period luminosity law
are shown by the graphs in Figure 4.
Of course the period of a variable star in distant
galaxies is really difficult to measure and so yet another method was needed to push back
the limits of cosmic distance measurement.
The Tully-Fisher
relationship
This relationship, named after the two American Astronomers who
discovered it, is not yet widely used because of lack of reliable data. It states that the more
luminous a galaxy the faster it rotates. Therefore measurement of the rotational speed of
galaxies using the Doppler effect gives a way of determining their distance from
us.
Astronomers therefore have to turn to the work of Edwin
Hubble.
