Distances |
(Think about these carefully before you consult the answers below)
QUESTIONS
1) Tycho did some remarkable work in his observations of the planets. From it Kepler derived his laws of planetary motion. Why then couldn't Tycho measure the parallax of stars or planets, and thus their distances? <answer>
2) To find the true distances to the planets, astronomers first had to find the distance to the Sun, which was done in a bit of a round-about way using the transits of Mercury and Venus already mentioned. Ironically, we are now able to measure the distance to the Sun much more accurately by first measuring the distances to the planets using radar, and then working backwards to find the distance to the Sun through Kepler's Laws. Why not just use radar to measure the distance to the Sun directly? <answer>
3) When giving the distances of the planets from the Sun, such as in the appendix table in your book, what are do the numbers actually mean? <answer>
4) Will the planets always orbit the Sun at their same distances as they are today? <answer>
5) There have been stories of another planet, some say a twin of the Earth, orbiting the Sun directly opposite the Earth and thus forever lost to our sight in the solar glare. However, space probes orbiting the Sun have failed to show any evidence of this hypothetical planet and it assuredly does not exist. On th e other hand, could such a planet be possible at the Earth's distance from the Sun and always the same distance from Earth? <answer>
6) What about Bode's Law? Why are astronomers so wary of it? <answer>
ANSWERS
1) People have difficulty in imagining the enormous distances between stars, and the smallness of parallactic angles. Think of this. The Sun is about 1.4 million km (865,000 miles) across. If we could shrink the Universe down such that our Sun was the size of a BB (about 3 mm or 1/8 inch), then Earth would be microscopic and roughly a foot away. The very nearest star would still be 57 miles away! Can you imagine how small a parallactic angle that would be? Well, the parallax of the nearest star is less than 0.8 arc seconds. This is about 75 times too small for the unaided human eye to discern, and is even too small for a six-inch telescope to resolve. (This doesn't even consider the effects of our turbulent atmosphere, which makes everything more difficult.) Even when Galileo built his first telescope, it wasn't powerful enough to help measure the parallax of stars. so no matter how good his observing skills, Tycho could not have measured the distances to stars using parallax. Measuring the distances to planets using parallax is greatly complicated by the motion of the planet itself, pretty much rendering the idea useless to the ancients even though the planets are vastly closer. (However, can can do such things today -- see the activity listed under "Parallax" (to accompany chapter 12).
3) Distances to the Sun are given in terms of the "semi-major axis" of the orbit, effectively the average distance of the planet from the Sun. Planets with more elliptical orbits, such as Pluto, can vary significantly in their distance from the Sun at any given moment. Venus, which has a nearly circular orbit, doesn't depart much from the semi-major axis distance. The Earth's orbit, which is a bit less circular than Venus' orbit, varies from a minimum of about 147,000,000 km to a maximum of about 152,000,000, and has a semimajor axis of about 149,600,000 km (figures are rounded off).
4) Recent mathematical theory (chaos theory) has cast doubt on the long-term stability of the solar system. While any catastrophic changes are not likely in our lifetimes -- probably not for at least 10s of millions of years -- it certainly is conceivable that the planets will change positions in relation to the Sun. Although we are not aware of any significant change in the average distance of the Earth to the Sun (which, however, is possible), there is evidence of several cyclical changes in the Earth's orbit. The eccentricity of the orbit changes, which alters the minimum and maximum distances of the Earth from the Sun, in a period of roughly 100,000 years. The direction of tilt of the Earth's axis, which will make the star Vega our North polar star in about 13,000 years, changes as well. Also the amount of tilt of the Earth's axis varies by nearly 3 degrees in a 40,000 year cycle. These changes likely affect the climate, but do not in themselves alter the average distance of the planet from the Sun.
6) In a world with so many charlatans and unproven ideas, scientists have learned to be conservative. In general, things are not accepted without solid evidence and explanation. When the evidence and explanation are not forthcoming, the event or phenomenon cannot be blindly accepted as true. For instance, while many astronomers believe in the strong likelihood of intelligent life elsewhere in the Universe, there is absolutely no concrete evidence of it. Lots of people say that they have seen or even met aliens, but none have any good proof of it. Should we accept it on hearsay? What about people who claim to have seen ghosts, leprechauns or fairies? Bode's Law may seem reasonable, but the only evidence we have for it is circumstantial. Just as in a court of law, in the court of science circumstantial evidence is not enough.
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