For relatively nearby things, like airplanes, we can use radar waves to measure how far away they are. Radar waves are like the radio waves that radios, wi-fi, and TVs operate with.
Distance By Parallax
The position of an object seems to change when you change your point of view. This is the basis for another distance measuring method. Imagine that your thumb is a “star” and hold your “star’ out at arm’s length. Look at your star against the background of the other more distant things. Without moving your arm or head, look at your star first through one eye and then the other eye. Does the star seem to shift position against the background stars? The shift in position is known as parallax.
The first people who tried to measure parallax of stars observed stars from different cities very far from each other. But they saw no shift at all. The stars were too far away for any parallax shift in position to be noticeable. They were able to measure the parallax shift for the Moon hundreds of years before radar was invented. In 150 BC, the Greek astronomer Hipparchus used parallax to measure a distance to the Moon that was only a percent different from the number we can measure today. Pretty good for someone 17 centuries before the invention of the telescope!
Measuring the parallax of the planets required much better angle-measuring techniques, and it wasn’t until 1672 that French astronomers just barely succeeded in measuring the parallax of Mars, and at last we knew how big the solar system is. The relative distances of planets from the Sun was known since the time of Johannes Kepler in 1610. So once the distance to Mars was measured, we also knew that the Sun is 150 million kilometers away from Earth!
But any baseline on Earth was not long enough for making a parallax measurement to determine distances to stars.
Distances to Stars By Parallax
After many failures in attempting to measure distance to stars by the parallax technique, a breakthrough came when astronomers realized that the fact that Earth itself changes position in space as it travels around the Sun could be employed as a very large baseline.
As the Earth travels around the Sun each year, we change our point of view by the diameter of Earth's orbit—over 300 million kilometers! Now that’s the kind of baseline we need to see the parallax of a star. When astronomers take pictures of the same region of sky six months apart, some stars—the closest ones to us—appear to change position with respect to the more distant stars.
Astronomers tried to use parallax on the stars in the 15th, 16th, 17th, and 18th century: and they all failed. Even with the enormous baseline of the diameter of the Earth’s orbit, the parallax to the brightest (and presumably nearest) stars always came out to be 0 degrees. They were back to having to assume all the stars were infinitely far away.
Finally in 1838 Friedrich Bessel, after a year and a half of observations of one star, 61 Cygni, succeeded in measuring the parallax to a star. The parallax was less than 1/10,000 of one degree! No wonder it was so hard to measure. Bessel calculated that 61 Cygni, one of the nearest stars to us, was an incredible 25 TRILLION kilometers away. That’s 25 thousand billion kilometers!
Units of Huge Distance
A convenient unit for describing such large distances is not kilometers, or even light seconds, light minutes, or light hours, but light years. Astronomers have found that the star which makes the biggest jump every six months is Alpha Centauri. It is “only” 41 trillion kilometers away.
4.6. How many light years is the distance to Alpha Centauri?
(Hint: How many kilometers are in a light-year?)
Bessel was only off by a factor of 4; 61 Cygni is actually about 100 trillion kiliometers away.
How many light years away is 61 Cygni?
The technique of measuring distances to stars by parallax led to another convenient unit for expressing distance: the parsec. A parsec is the distance to an object that has a parallax angle of 1 arcsec with a baseline of 1 AU (astronomical unit, the average distance from Earth to
Sun). The word “parsec”comes from a combination of “parallax” and “arcsecond.”
Beings outside of our galaxy would see it made of billions of stars (plus assorted gases and dust) and shaped like a big spiral—a pinwheel. Might it not be spinning like a big pinwheel? Indeed it is. But for the galaxy to spin, each star must orbit the center of the galaxy. They don’t all move in perfectly synchronized orbits though, so from our vantage point stars seems to move very slowly with respect to each other. The motion has two components to it: lateral (sideways) movement and movement towards or away from us. The sideways motion is called proper motion, though no one seems to know anymore what’s proper about it. When we measure a star’s velocity towards or away from us, it’s called radial velocity (as in change of length of a radius line of a circle where we’re at the center and the star is on the circle).
Star Brightness and Magnitude
For really faraway stars, yet another clever distance finding method had to be found. The next trick to determine star distances was to compare their brightness.
The Magnitude Scale
An ancient Greek astronomer, Hipparchus, devised a system to classify stars according to their brightness. He divided all of the stars he could see on a dark, clear night into six groups with magnitude 1 stars being the brightest group and magnitude 6 stars being the dimmest. Hipparchus did not have a telescope back in those days, so the stars he classified were only those visible to the naked eye. Astronomers still use the magnitude scale to describe the brightness of stars. Since human eyes see light in a logarithmic fashion, the mathematics of the magnitude scale is based on logs.
When using SalsaJ image processing software to measure brightness of a star in a CCD image, you use the photometry tool to obtain the star's intensity (brightness). To see the magnitude scale in terms of this intensity value, let’s assume a magnitude 0 star has brightness = 10000 (note: we are just using an arbitrary value to demonstrate the scale). Based on this brightness value, the chart shows magnitudes with the associated brightness.
Photometry is the process of measuring the amount of light received from an object. When you display an image using SalsaJ or HOU Image Processing software, you can use the cursor to see the amount of light registered by each pixel in the image. This value is related to the number of photons striking each pixel in CCD camera.
With the Photometry tool in SalsaJ, routines
add up all the values within a specific area of pixels to give the
total intensity value for a star. The routines are designed to subtract
background light and give only the intensity value created by the star
itself. However, this is not to be confused with the magnitude brightness of the star. To avoid being confused by photometry terminology, study the definitions below.
Definitions of Photometry words
Cepheid Variable Stars as Distance Indicators
In 1784 a star in the constellation Cepheus was observed night after night by John Goodricke, and he noted that the star became brighter and then dimmer. The fluctuation in brightness repeated over and over again approximately every five days. This was the discovery of the first Cepheid variable star.
In 1908 at Harvard College Observatory, Henrietta Leavitt was examining many photographic images of the Magellanic Clouds, two small galaxies orbiting the Milky Way. She was studying the Cepheid variable stars in the Magellanic Clouds and noticed a pattern in their brightness fluctuations: the brightest Cepheids had the longest fluctuation cycles and the dimmest stars the shortest fluctuation cycles. Since the Cepheids were all in the Magellanic clouds, all at the same distance from us, comparing their apparent brightness was equivalent to comparing their luminosity (see definitions in box at right). Leavitt arrived at a general relationship between luminosity and period which she published in 1917. It is now called the period-luminosity relationship, illustrated in the diagram below and in the investigation A Cepheid Variable Star below.
The period-luminosity diagram allows us to determine the luminosity of a Cepheid simply by measuring its period of brightness fluctuation. This is incredibly valuable for determining distance, because we can compare apparent brightness of a star with its luminosity—a comparison that hinges critically on distance. The farther away the star, the dimmer its apparent brightness is, in accord with an inverse square law. Leavitt’s discovery of the period-luminosity relationship is a milestone in astronomy. Before her research, no one had a reliable tool for measuring the distance to objects farther away than the closest stars.
To measure the period of fluctuation, the Cepheid must be observed at least every few nights for several weeks. The light intensity measured for a Cepheid will change from night to night for two reasons:
In order to get a plot of the Cepheid’s changing luminosity you must
remove the effects of the atmosphere by including a reference star.
Since the Cepheid star and the reference star are on the same image, the
observing conditions are the same for both stars. If the observing
conditions did not change from night to night, the reference star would
appear just as bright each night. In general, observing conditions do
change, so the number of Counts measured for the reference star will
increase or decrease depending on how much light the atmosphere lets
through. If the atmosphere blocks out a large amount of light on one
night, both stars will appear dimmer; on a clear night, both stars will
We’ll find out more about uses of Cepheid variable stars in Chapter 9, The Universe Begins ... and Ends?
The Nearest 100,000 Stars,
an online interactive with which you can explore stars
in the Milky Way that are in the vicinity of the Sun.
Edward L. Wright. The ABC's of Distances - http://www.astro.ucla.edu/~wright/distance.htm