Part 1
This will be a 2 part discussion about the Cosmic Distance Ladder. Part 1 will cover the Parallax method, Spectroscopic parallax, and Main sequence fitting as methods to determine the distance of stellar objects from Earth. I will begin by defining some astronomical units of measure and then discuss the techniques used to measure the distance of objects throughout our Solar System, the Milky Way galaxy, and the Universe.
Part 2 will focus on the use of variable stars, such as Cepheids and RR Lyraes, as well as nearby galaxies. We will also explore The Tully-Fisher Relationship, and Hubble’s Law to determine the distance of objects deep in our universe. I hope that after reading part 1 & 2 you will have a better understanding of how the distance of objects from our Solar System to the ends of the Universe are determined.
The moon is roughly 250,000 miles from Earth, the sun is 93 million miles from the Earth or 1 astronomical unit away (AU). The next nearest star to the Earth, Proxima Centauri is 4.3 light years (ly)away. The Milky Way Galaxy is 30,000 parsecs (pc) or 30 kiloparsecs (kpc) measured from one side to the other. What do some of these units of measure such as light year, astronomical unit, and parsec mean? How do we actually know how far these objects are from Earth or how far apart they are from each other?
Astronomical Units of Measure
1 AU of astronomical unit is equal to the average distance between the Earth and Sun which is 149,598,000 km (92,955,887 miles.) This unit is used to describe distances within our solar system. Neptune, for example, is 30.1 astronomical units from Earth. This equates to about 2,700,000,000 miles. It is much easier to to calculate using 30.1 au then it is to use 2.7 billion miles.
1 ly or light year is the distance light travels in a year. It may sound as if it is a measure of time but it is actually a measure of distance. 1 light year is equal to 5,878,630,000,000 miles. It is much easier to think and calculate using light years when dealing with the enormous distances associated with the universe.
The Hertzsprung-Russell diagram or HR diagram is “… a graph that is used for making stellar calculations. It gives the relationship between the luminosity of stars against their type and temperature” according to https://universavvy.com/astrophysics-hertzsprung-russell-diagram-explanation. This diagram can be used to classify, trace the life cycle, as well as teach about the how stars work.
Stellar Parallax and the Parsec
In order for our discussion of parsec to make sense I am going to discuss the phenomena of parallax first and then tie it into our description of a parsec. On the cosmic distance ladder, parallax is the only direct method we have to measure distances to stars. To give you an easy and quick example of parallax hold one arm straight out in front of you and point your thumb to the sky. Now alternate opening and closing your right and then your left eye. The apparent movement of your thumb is an example of parallax.
Astronomers can use this idea to measure the distance of a star. In the image below you can see the position of the Earth six months apart. The angle of parallax can be measured by comparing how the star has shifted as compared to the stars behind it. You can see that a triangle has been formed between the star and the two positions of the Earth six months apart. By using some trigonometry you can determine the distance to the star. This method of measuring distance is limited because the parallax angle for more distant stars is to small for us to measure.
1 pc or parsec is equal to 3.26 ly or 206,280 AU. I know what you are thinking, Han Solo said about the Millennium Falcon “it’s the ship that made the Kessel run in less than 12 parsecs.” https://youtu.be/fjYuw6zWk_Y Maybe “in a galaxy far, far away” a parsec is a measure of time, but in our galaxy it is a measure of distance. The definition of 1 parsec is the distance to an object which has a Parallax angle of 1 arscencond. You can see the term parsec is a combination of parallax and arcsecond. To measure the distance, in parsecs, using parallax angle you use the equation d = 1 AU/p” where p is the parallax angle. Your answer will be the distance in parsecs. This method of calculating distance only works for stars that are within roughly 300 parsecs or 978 light years from Earth, beyond that distance the parallax angles are to small to measure.
Spectroscopic Parallax
According to https://www.atnf.csiro.au/outreach/education/senior/astrophysics/photometry_specparallax.html “The term spectroscopic parallax is a misnomer as it actually has nothing to do with parallax. It is, however, a way to find the distance to stars. Most stars are too far away to have their distance measured directly using trigonometric parallax but by utilising spectroscopy and photometry an approximate distance to them can be determined.”
So then what is spectroscopic parallax and how does it help us determine the distance of stars? Astronomers determine the spectral and luminosity class of a given star. Using photometric equipment the apparent magnitude and color index can be determined. The star is placed on to the HR diagram and its apparent magnitude is deduced. At this point an equation called the distance modulus equation is used to determine the distance in parsecs of the star. According to Australia National Telescope Facility “In practice this technique is not very precise in determining the distance to an individual star…..Nonetheless it is still an important methods for estimating distance to stars beyond direct trigonometric parallax measurement.”
Main Sequence Fitting
Main sequence fitting as a method of determining cosmic distance is done by comparing the relative distance of open clusters to the distance of the Hyades galaxy which has a known distance. An open cluster according to https://www.sciencedaily.com/terms/open_cluster.htm is “a group of up to a few thousand stars that were formed from the same giant molecular cloud, and are still loosely gravitationally bound to each other.” The stars in these clusters are believed to have been formed at the same time and located the same distance away from Hyades. The distance of Hyades was found via direct measurement using stellar parallax.
Scientists will measure the spectra of the cluster to determine “spectral type, luminosity, and temperature and define a main sequence” according to Teach Astronomy https://www.youtube.com/watch?v=hq29cjeR2o4. Scientists compare the shift between the open cluster and the Hyades galaxy on the HR diagram and use the inverse square law to determine the relative distance between the open cluster and the Hyades galaxy. The inverse square law states that the the light will get dimmer by a factor of the square of the distance away from the source of light.
Next week we look at part 2 of the Cosmic Distance Ladder which should give you a fuller picture of how astronomers determine the distance of objects throughout our universe.







