# (10a) The Scale of the Solar System

 Index   8b. Parallax 8c. Moon dist. (1) 8d. Moon dist. (2) 9a. Earth orbits Sun? 9b. The Planets 9c. Copernicus         to Galileo 10. Kepler's Laws Kepler's Laws         (For teachers) 10a. Scale of Solar Sys. 11. Graphs & Ellipses 11a. Ellipses         and First Law 12. Second Law 12a. More on 2nd Law   12b. Orbital Motion Kepler's laws agree with all observed planetary motions, and by the table in the previous section, they give the correct proportions of all planetary orbits. If the mean distance of Earth from the Sun is 1 AU ("Astronomical Unit"), then that of Venus is 0.723 AU, of Mercury 0.387 AU and that of Mars is 1.524 AU. But how much is that in kilometers, or miles? In other words--what are the actual dimensions, not just their proportions?   Tycho still accepted the erroneous estimate by Aristarchus of the Sun's distance, 20 times smaller than the actual one (see section about Aristarchus). Soon afterwards the telescope was discovered, and starting with Galileo, astronomers realized that Venus appeared as a round disk (or a crescent, when near Earth and presenting mostly its dark side). At its closest, Venus is nearly one minute of arc (1/60 degree) across. Assuming it was about as big as Earth, and using (for instance) Kepler's laws, it was possible to estimate the distance of Venus, and from it, the distance of Earth from the Sun. That led to a much better estimate of about 15,000 Earth radii (see "Halley's Admonition" in David Seller's excellent web site, based on his book on the transits of Venus), more than 12 times the estimate by Aristarchus but still too small.   If we know the proportions of all the orbits in the solar system, measuring just one actual distance in kilometers gives the scale of all orbits around the Sun. What one needs is a parallax, that is, an observation of a planet where the small difference in viewing angle, between two widely separated points on Earth, makes a measurable difference. Remember how Hipparchus estimated the distance of the Moon? In a solar eclipse which was total in one location, at another location about 1000 kilometers away, only 80% of the Sun was covered. The body blocking the Sun--the Moon--was close enough that moving an observer by about 1000 kilometers shifted its apparent position in the sky by 1/5 the apparent size of the Sun, or about 0.1 degree.

Next Stop: #11. Graphs and Ellipses

Author and Curator:   Dr. David P. Stern
Mail to Dr.Stern:   stargaze("at" symbol)phy6.org .

Last updated: 9-18-2004