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Can I invoke the standard statement which used to be used for freeware ;

You are, of course, welcome to consult and make use of my pages at will. However, if you have found them useful in any appreciable way, please consider sending a small disbursement (even something as small as 1 Euro/Pound/Dollar/etc. would be received with appreciation).

B. Daugherty, 31 MH, Portsmouth PO5 3JG, Britain.

The Distance Ladder


This method uses the same method as used by surveyors to calculate distances, by taking bearings on the same object from two different locations separated by a known distance.

In this case, the baseline will be diameter of the Earth's orbit (300 million km). A bearing is taken at a particular time, and six months later, when the Earth is 'over the other side' of its orbit, another bearing is taken.

This can only be used for 'nearby' stars, but was famously performed for the first time in 1831 by Bessel in the former German city of Königsberg (the present-day Russian city of Kalinningrad). This was the first formal proof that the Sun is the center of the Solar System - about 300 years after the idea had been first mooted by Copernicus. The star he used was 61 Cygni, which was known to have a large proper motion.

Shortly after Bessel's achievement, Thomas Henderson measured the distance to Alpha Centauri.

The relevance of this method has been extended further out to by the space probe Hipparcos.


If an object has a parallax of one second of arc (where 1 second = 1/3600 degree), it is at a distance of 1 parsec. By parallax, I mean the method described in the previous section where bearings are taken on an object six months apart, the parallax being the angle subtended by the object.

star's distance (in parsecs) = 1/parallax (stated in seconds)

One parsec is equal to 3.26 light years.

General information:

1 degree = 60 minutes
1 minute = 60 seconds


These type of stars are mentioned under Evolution. Since their pulsations are an indication of their intrinsic magnitude, they can be used as distance indicators by comparing their intrinsic magnitude with their apparent magnitude as viewed from Earth.

Cepheids were used by Hubble in his work in showing that galaxies existed outside our own. He placed M31, the Andromeda Galaxy at a distance of around 1 million light years. During the war, Walter Baade modified this distance to about 2 million light years, doubling the size of the Universe in the process, and also removing the problem of why the Milky Way appeared to be so anamolously large. Baade had been excused war duty as an 'alien' and also apparently had the advantage of using Mount Wilson telescope with the lights of Los Angeles blacked out. Hubble had originally made his distance measurement when they had been unaware that there were different types of Cepheid.

Nowadays, M31 is placed at about 2.2 million light years.

Cepheids have periods of 1 to 50 days. Their period of pulsation is directly related to their intrinsic luminosity. The brighter a star is intrinsically, the longer is its period of pulsation.

This was first discovered by Henrietta Swan Leavitt in 1912. She discovered the law by studying Cepheids in the Small Magellanic Cloud and used the valid assumption that all the Cepheids she was studying were at the same distance. But it still required scaling before this discovery could be used for practical purposes. At the time they had no idea of the distance to the Magellanic Clouds.

The nearest Cepheid is Polaris. It varies between magnitudes 2.5 and 2.6 every 4 days. Cepheid Light Curve

Several subgroups of Cepheids are now recognised. Classical Cepheids occur an area on the Hertzsprung-Russel diagram known as the Instability Strip.

See Distance Ladder for information on the application of Cepheids to distance determination.

From a historical viewpoint, I should mention that the first Cepheid was discovered in 1784 by a teenager John Goodricke (who, as is always mentioned in the commentaries, was also deaf and dumb). This was δ Cephei

HR Diagram showing Cepheida and T Tauri Regions

RR Lyrae

RR Lyrae are similar to Cepheids but their periods are much shorter, measured in hours. They are Population II of spectral type A or F - about half are found in globular clusters.

Red Shift

Measuring the Doppler Shift produces a measure of the Red Shift - a 'Red Shift' because practically all galaxies are moving away from us. Only objects near to us are likely to exhibit a Blue Shift if their motion towards us is greater than the overall universal tendency to move away from us.

This red shift produces an accurate measurement of relative distances to bodies over very large distances, in other words it could tell accurately that a particular object is twice as far away as another object and the like, but it relies for its absolute values of distance on the methods used for smaller distances. If these other methods that it bases itself on are producing inaccurate or uncertain values for distance, then the red shift is likely to be out as well, by virtue of the knock-on effect.

Twenty-Five Brightest Stars

Star Constellation Type Abs. Mag. Dist. (LY)
1 Sirius Canis Major A 1.5 8.8
2 Canopus Carinae F -4.7 196
3 α-Centauri Centaurus G,K 4.1 4.3
4 Arcturus Bootes K -0.3 36
5 Vega Lyra A 0.5 26
6 Capella Auriga G -0.6 46
7 Rigel Orion B -8.2 815
8 Procyon Canis Minor F 2.7 11
9 Achernar Eridanus B -1.3 127
10 Betelgeuse Orion M -5.9 650
11 Hadar Centaurus B -4.3 390
12 Altair Aquila A 2.4 16
13 Aldebaran Taurus K -0.6 69
14 Acrux Crux B,B -3.4,-2.9 260
15 Antares Scorpio M,A -5.0 425
16 Spica Virgo B -2.9 260
17 Formalhaut Piscis Austrinus A 2.0 23
18 Pollux Gemini K 1.0 36
19 Deneb Cygnus A -6.2 1630
20 Mimosa Crux B -4.5 490
21 Regulus Leo B -0.6 85
22 Adhara Canis Major B -5.0 650
23 Castor Gemini A 0.8 46
24 Shaula Scorpio B -3.4 325
25 Bellatrix Orion B -3.3 303

Crab Nebula

Big Red Spot on Jupiter