Distances to the Planets |
Today we can gauge the distance to the Moon and
nearby planets extremely accurately using radar and, in the case
of the Moon, with lasers. Since radar signals travel at a
precisely known speed (the speed of light), all we have to do is
time how long it takes for the signal to get to, say Venus, and
back to the radar antenna on Earth. Half that time is how long it
takes to get from Earth to the planet. Then all you need do it
multiply that time by the speed of light. (There is an example in
our Activity .)
The Apollo astronauts in the late 1960s and early 1970s left several arrays of "retroreflectors" on the Moon. These are arrangements of prisms that reflect light back in the exact direction it came from. Using powerful lasers on Earth, astronomers can bounce laser beams off the retroreflectors, and time how long it takes for the beam to be reflected back. Since the laser travels at the speed of light (just the same as the radar beam), half the round-trip time multiplied by the speed of light yields a very precise distance to the Moon -- down to a few centimeters!
In ancient times there were no laser and no radar. Ancient astronomers recognized the effect of parallax (see chapter 1 and later in chapter 12) and its potential use, but the stars were too far way for the ancients to utilize this method on them. Even the planets, which the ancients guessed to be much closer because of their motions, were too far for accurate distance determination by parallax.
But based on the work of Polish astronomer Nicolaus Copernicus, and the observations of Danish astronomer Tycho Brahe, German mathematical astronomer Johannes Kepler developed his famous mathematical laws of planetary orbits (chapter 1). His third law gives a way of determining a planet's relative distance to the Sun simply by observing how long the planet takes to orbit the Sun. However, it says nothing about the exact distance. It says, for instance, that Jupiter on the average is 5.2 times as far from the Sun as the Earth is, but not the exact distance. In order to gauge the distance to the planets, then, we must know the distance to the Sun.
In the 1670's, astronomers measured the parallax of Mars, which led to a determination of 87,000,000 miles as the distance to the Sun. The famous astronomer Sir Edmund Halley of cometary fame suggested observing Mercury or Venus as they passed directly in front of the Sun. (Such passages are called transits and they are not common. There are about 14-15 transits of Mercury per century, with one on November 15, 1999. The next two are May 7, 2003 and Nov. 8, 2006. Transits of Venus are far rarer, there having been only six since the invention of the telescope! The last was in 1882 and the next will be on June 8, 2004.) Halley didn't live to complete the observation, but others, including the famous British naval Captain James Cook, observed the 1769 transit of Venus. There was some discrepancy in the results from various observers, but a reasonably accurate distance to the Sun (about 95 million miles) was derived from the data in 1835 by the astronomer Encke.
Today we can measure parallax more accurately, and the distance to the Sun has been refined to about 150,000,000 km or 93,000,000 miles. Knowing the Earth's distance to the Sun, called an Astronomical Unit , it is easy to apply Kepler's 3rd Law (chapter 1), to determine planetary distances. Take a look at table 1.2 in chapter 1. It shows that according the Kepler's Third Law, Mars is 1.52 times the distance of the Earth to the Sun. Hence Mars' distance to the Sun is 1.52 times 150 million kilometers, or about 228 million miles from the Sun. But in Kepler's time the estimates of the distance to the Sun were considerably off, so the planetary distances were, too.
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