EarthRise

photographed from lunar orbit. The distance to the moon in earth diameters has a surprising physical meaning. Just as the visual size of the moon is measured on earth as being 110 diameters away, the visual size of the earth viewed by an astronaut on the moon is 30 diameters away, or 3.7 times the visual size of the moon from your backyard. Impressive.

As you watch the moon rise from the horizon to overhead, you're actually getting closer to it. Draw a diagram of earth and moon like that on the previous page, and look at the distances to the moon from various points on the earth's surface. For each point, where does the moon appear relative to the local vertical (a line to the center of the earth)? As the earth turns toward the point where the moon is on the vertical, you (and the ground you're standing on) are carried through space toward the moon. Ah, just how much closer?

That astronaut on the moon...does he see the earth rising like we see the moon rising?

Further Browsing

You may have noticed that we found the distance to the moon only in earth diameters, not in something like meters or cubits that's more human-size. This is how the ancient Greeks did it, because it's a separate project to find the size of the earth, with its own experimental uncertainties. For centuries they argued how many stades or parasangs in the earth's circumference. The effort most famous today was by Eratosthenes, neither the first nor the last, but the most picturesque. If you'd like to find out how big the earth is with a Web-pal, try the Noon Project: Eratosthenes online!

The moon's distance actually varies almost plus or minus two earth diameters over the course of a month (its orbit is an ellipse, not a circle). You can see this by looking at photographs of the moon at the same scale, taken at different distances. From day to day over a month, along with the varying illumination, the size of the containing circle varies a little because of the changing distance. Measure the sizes carefully and plot the inverses (the ranges) on polar graph paper: you get an ellipse! An astronomy prof has an animated set of photos linked at the bottom of that page.

The dragon's mouth of an eclipse can be photographed in surprising ways: here's the coolest photo from space of the eclipsed moon, which is actually scientifically informative. Links to nitty-gritty eclipse info and pictures.

Knowing the distance to the moon, how long would it take you to travel there? Time was a critical issue for the astronauts in the crippled spacecraft Apollo 13: they were running out of supplies. A little earlier, Jules Verne described an exciting voyage to the moon that tried to be scientific.

Today scientists know and can predict the (constantly changing) distance to the moon within inches, by timing light pulses from the laser reflector left on the moon by the astronauts. This is not overdoing it: they actually measure a lot of important physics.

And for general stuff about the sun, moon, and planets, the Web is crawling with info and good pictures. Try The Nine Planets. Nice online and free software to show the positions of the moon and planets at any time at John Walker's (he started a major software company and is now retired). I would be remiss in not noting our own CPO Dessert Tray of cool science and math links.

'Course, there are books, too...;) More details in Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley, by Albert Van Helden, who has a nice Web site on Galileo. The book gives the details and tacit assumptions we zoomed over here, like how the Greeks knew the sun was much further away than the moon, even if not exactly how far. (The telescope needed to be invented to find the distance to the Sun) The Greek technique was called "lunar dichotomy". Hint: the half-moon is due south at sunset when the days and nights are equal. There's hard-core nitty-gritty in On the Distances Between Sun, Moon, and Earth According to Ptolemy, Copernicus, and Reinhold, by Janice Henderson (ISBN 9004093788).

Return to CPO Home page