# Measuring the distance of stars

1. Aug 27, 2004

### neoweb

Is the parallax method still the one most widely used (for the relatively nearer stars at least)? More particularly, is it still the case that we take one measurement then wait six months until the earth is on the other side of the sun and take a second measurement? Or has this been superseded by something else?

Also, with the parallax method we need to know the distance from earth to Sun - so how did we first figure out how far away the Sun is?

2. Aug 27, 2004

### Janus

Staff Emeritus
If you measure the position of the stars you will note that they have an apparent displacement which is greatest when the Earth is moving at a right angle to the light arriving from the star. This displacement is caused by the aberration of light and its angle depends on the Earth's orbital velocity. Measuring this displacement allows us to determine the Earth's orbital velocity. given the length of the year and the orbital velocity, we can calculate the circumference of the Earth's orbit, and dividing this by 2 pi gives us the mean radius or distance from Sun to Earth.

3. Aug 27, 2004

### Chronos

The earth to sun distance was first estimated by a dude named Aristarchus about 2300 years ago. Parallax was the first method used to gage the distance to other stars. It is arguably the most reliable since it relies on well known and accepted geometrical principles. It is still useful today. Other more sophisticated methods came into use more recently. The first method to emerge after parallax was the Cepheid yardstick. See here for more information.
http://curious.astro.cornell.edu/question.php?number=400 [Broken]
http://curious.astro.cornell.edu/question.php?number=128 [Broken]

Last edited by a moderator: May 1, 2017
4. Aug 27, 2004

### Nereid

Staff Emeritus
Yes. http://astro.estec.esa.nl/Hipparcos/ [Broken] has given us probably the most accurate distances to nearby stars to date. The principles on which it worked (the satellite has long since burned up) are a little arcane, but at the core is parallax.

The 'first' methods of determining the distance to the Sun were also parallax, but in an interesting way - a Greek astronomer (Aristarchus?) estimated the distance to the Sun by the shadow of the Earth on the Moon, during a lunar eclipse! (It's simple geometry). However, as several of his input parameters were wrong, he got the distance to the Sun wrong too.

More generally, since the Moon and Sun have the same angular diameter (as evidenced by solar eclipses), some simple geometry shows that once you have one distance (e.g. Earth to Moon), you can get the other. It gets a bit more complicated if you want to get accurate (e.g. orbits aren't perfect circles).

With Newton and accurate orbits of the planets and asteroids, the distance to the Sun was fairly accurately determined; however, only when radar astronomy was able to get an echo (from Eros, IIRC, though it might have been Venus) could the solar system distance scale be nailed down to ~km (or maybe more accurately). Today we have transponders on interplanetary probes, and the 'light return time' gives very accurate distances (we also need good ephemerises). Anyway, the distance to the Sun need not be all accurately known to work out distances to nearby stars ... the parallax angle (pre-Hipparcos) could only be measured to ~1 decimal place!

Last edited by a moderator: May 1, 2017
5. Aug 27, 2004

### Phobos

Staff Emeritus
From what I understand....

Parallax is still used to give very good measurements for anything in the range of nearby stars (dozens of light years away). After that, distance measurements to stars in the galaxy become more uncertain and are often cross-referenced to various observations/calculations methods in order to reach a satisfactory answer (e.g., comparisons to other stellar distance measurements). Then Cepheid variables begin to help us out as a "standard candle" that can help improve measurements out to the nearby galaxies. After that, astronomers use supernova 1a as the next standard candle to get pretty good measurements of the more distant galaxies (perhaps +/- 10%?). Couple that with redshift measurements.