Jim's Corner Blog

The Cosmic Distance Ladder

The cosmic distance ladder and how astronomers determine celestial distances is often misunderstood by most amateur astronomers.  The cosmic distance ladder is a succession of different methods used by astronomers to determine distance to deep space objects.,

Basically, there are four different methods used.

  1. The trigonometric parallax method – The most important fundamental distance measurements come from trigonometric parallax. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an isosceles triangle, with the distance between the extreme positions of Earth’s orbit around the Sun forming the base of the isosceles triangle and the distance to the star being the equal length sides to complete the triangle.  Precise measurements of angles and simple trigonometry calculations yields the distance to the object.  This method has proven relatively accurate for stars and deep sky objects up to 1,000 light-years.
  • Cepheid Variables Luminosity method –  Understanding the use of Cepheid variables to determine distance is often glossed over in many astronomy books.  The following is an attempt to address the use of Cepheid Variables in distance calculations. By definition, a Cepheid Variable is a star that pulsates radially, varying in both diameter and temperature, thus producing changes in brightness with a well-defined stable period and amplitude.  Or, in another way to describe it, Cepheid Variable stars are intrinsic variables which pulsate in a predictable way. In addition, how often a Cepheid star pulsates is directly related to its luminosity or brightness.  The discovery of the relationship between luminosity and period was made by Henrietta Swan Leavitt, during her tenure as one of the “Harvard Computers”.   Beginning in 1893, Edward Charles Pickering, the Director of the Harvard College Observatory, hired a group of highly educated and skilled women to help him process astronomical data and data analysis using the large number of photographic plates that had been accumulated by the observatory.  The “human computers” became known as the “Harvard Computers”.  Joining Leavitt were Williamina Fleming, Annie Jump Cannon, Antonia Maury, and many more. Two types of Cepheids are used for distance measurement.  The Type I Cepheid variables is also known as the Classical Cepheid.  Type I Cepheids are yellow bright giants and supergiants that undergo pulsations with very regular periods on the order of days to months.  Longer period Type II Cepheids are more luminous, and follow a different luminosity-period curve.  By knowing the period of a Cepheid Variable, the astronomer can refer to the luminosity-period curve to know the intrinsic luminosity of the star, and with the formula of interstellar light absorption calculate the distance.
  • Type 1a Supernova method – Type Ia supernovae are some of the best ways to determine extragalactic distances. Type Ia supernovae occur when a binary white dwarf star begins to accrete matter from its companion star. As the white dwarf gains matter, eventually it reaches its Chandrasekhar Limit of 1.4M, where M is the absolute magnitude.  Once reached, the star becomes unstable and undergoes a runaway nuclear fusion reaction. Because all Type Ia supernovae explode at about the same mass, their absolute magnitudes are all the same. This makes them very useful as standard candles. All Type Ia supernovae have a standard blue and visual magnitude of  -19.3.  Therefore, when observing a Type Ia supernova, if it is possible to determine what its peak magnitude was, then its distance can be calculated.
  • Redshift method – Many distant galaxies are so far away that Cepheid variables and Type 1a supernovas cannot be seen.  The redshift method is a result of Edwin Hubble’s “Hubble’s Law”, which states that the Doppler redshift of a distant galaxy is proportional to how far away the distant galaxy is from earthbound observers.  Hubble’s original value of what is now known as “Hubble’s constant” was extremely overestimated, due to his not knowing there were two types of Cepheid variables. Hubble’s constant has been revised over the years to its current value of 71.0±2.5 km/s/Mpc, with corrections needing to be made to take into account Einstein’s General Theory of Relativity.  Hubble’s Law is mathematically expressed as:

v = HD
v is the recessionalvelocity in km/s
H is Hubble’sconstant
D is the distance from the galaxy to the observer