Themes > Science > Physics > Astrophysics > Introduction to Astrophysics > Properties of Stars > Astronomical Unit


Although this was not listed explicitly in the basic Solar parameters section, this turns out to be a necessary number for the determination of the Solar radius and luminosity. The determination of the Astronomical Unit is fairly straightforward given that we know the scale of the Solar System based on Kepler's Third Law of Planetary Motion, that is, the orbital period squared of a planet is equal to semi-major axis of its orbit cubed if the orbital period is measured in years and the semi-major axis of the orbit is measured in astronomical units.

Period squared = a cubed

The orbital periods of the planets are easy to measure. Based on this information, we find that the sizes of the orbits of Venus and Earth are

  • Venus: a ~ 0.7 A. U.
  • Earth: a = 1.0 A. U.
and so the Earth, at closest approach, is 0.3 A. U. from Venus. This information, although useful, is not what we want. In order to meet our needs, we need to determine how many kilometers or miles or meters, ... are contained in 1 A. U. We accomplish this task as follows. We know that at closet approach the Earth is 0.3 A.U. from Venus.


Because we know how fast the beam of radiation travels (velocity = 300,000 km per second), we can determine how far away Venus is in terms of km.

Based on this type of experiment, we have determined that the astronomical unit is roughly 149,000,000 kilometers.

The distance will be used to determine the radius of the Sun and the luminosity of the Sun. In terms of other stars, knowing the distances to more distant stars is also crucial because it leads to the luminosities of distant stars. The exercise of finding distances to objects in the Universe turns out to be a crucial exercise for many subfields of astronomy. When we discuss Cosmology, we will return to this important topic.

Other than this direct method of determining distances to stars, the most reliable method is known as Annual Trigonometric Parallax (as discussed in Physics 207 last quarter). This method will be re-discussed next quarter in more detail.


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