 An important subfield of astronomy is astrometry: the study of positions and movements of celestial bodies

Yüklə 483 b.
 tarix 01.08.2018 ölçüsü 483 b. • • From the Sun to distant stars? • Usually, the indirect methods control large distances in terms of smaller distances. One then needs more methods to control these distances, until one gets down to distances that one can measure directly. This is the cosmic distance ladder. • But suppose we had no advanced technology such as spaceflight, ocean and air travel, or even telescopes and sextants. Would it still be possible to convincingly argue that the earth must be (approximately) a sphere, and to compute its radius? • Eratosthenes (276-194 BCE) computed the radius of the Earth at 40,000 stadia (about 6800 kilometers). As the true radius of the Earth is 6376-6378 kilometers, this is only off by eight percent! • Aristotle also observed that the terminator (boundary) of this shadow on the moon was always a circular arc, no matter what the positions of the Moon and sun were. Thus every projection of the Earth was a circle, which meant that the Earth was most likely a sphere. For instance, Earth could not be a disk, because the shadows would be elliptical arcs rather than circular ones. • Eratosthenes then observed a well in his home town, Alexandria, at June 21, but found that the Sun did not reflect off the well at noon. Using a gnomon (a measuring stick) and some elementary trigonometry, he found that the deviation of the Sun from the vertical was 7o. • High school trigonometry then suffices to establish an estimate for the radius of the Earth. • How far is the moon from the Earth? • The radius of the Earth, of course, is known from the preceding rung of the ladder. • From this and basic algebra, Aristarchus concluded that the distance of the Earth to the moon was about 60 Earth radii. • Since Aristarchus knew the moon was 60 Earth radii away, basic trigonometry then gives the radius of the moon as about 1/3 Earth radii. (Aristarchus was handicapped, among other things, by not possessing an accurate value for , which had to wait until Archimedes (287-212 BCE) some decades later!) • How far is the Sun from the Earth? • Nevertheless, these results were enough to establish that the important fact that the Sun was much larger than the Earth. • Since the distance to the moon was established on the preceding rung of the ladder, we now know the size and distance to the Sun. (The latter is known as the Astronomical Unit (AU), and will be fundamental for the next three rungs of the ladder). • Elementary trigonometry then gives the distance to the sun as roughly 20 times the distance to the moon. • How far is Mars from the Sun? • It required the accurate astronomical observations of Tycho Brahe (1546-1601) and the mathematical genius of Johannes Kepler (1571-1630) to find that Mars did not in fact orbit in perfect circles, but in ellipses. This and further data led to Kepler’s laws of motion, which in turn inspired Newton’s theory of gravity. • The angle between the sun and Mars from the Earth can be computed using the stars as reference. Using several measurements of this angle at different dates, together with the above angular velocities, and basic trigonometry, Copernicus computed the distance of Mars to the sun as approximately 1.5 AU. • Brahe’s observations gave the angle between the sun and Mars from Earth very accurately. But the Earth is not stationary, and might not move in a perfect circle. Also, the distance from Earth to Mars remained unknown. Computing the orbit of Mars remained unknown. Computing the orbit of Mars precisely from this data seemed hopeless - not enough information! • To compute the orbit of Earth, use Mars itself as a fixed point of reference! To pin down the location of the Earth at any given moment, one needs two measurements (because the plane of the solar system is two dimensional.) The direction of the sun (against the stars) is one measurement; the direction of Mars is another. But Mars moves! • By 1900, when travel across the Earth become easier, parallax methods (e.g. timing the transits of Venus across the sun from different locations on the Earth – a method first used in 1771!) could compute these distances more directly and accurately, confirming and strengthening all the rungs, so far, of the distance ladder. • Ole Rømer (1644-1710) and Christiaan Huygens (1629-1695) obtained a value of 220,000 km/sec, close to but somewhat less than the modern value of 299,792km/sec, using Io’s orbit around Jupiter. • Now the most accurate measurement of distances to planets are obtained by radar, which requires precise values of the speed of light. This speed can now be computes very accurately by terrestrial means, thus giving more external support to the distance ladder. • Einstein reasoned that Maxwell’s equations, being a fundamental law in physics, should hold in every inertial reference frame. The above two hypotheses lead inevitably to the special theory of relativity. This theory becomes important in the ninth rung of the ladder (see below) in order to relate red shifts with velocities accurately. • Maxwell’s theory that light is a form of electromagnetic radiation also helped the important astronomical tool of spectroscopy, which becomes important in the seventh and ninth rungs of the ladder (see below). • Ironically, the ancient Greeks dismissed Aristarchus’s estimate of the AU and the heliocentric model that it suggested, because it would have implied via parallax that the stars were an inconceivably enormous distance away. (Well…they are.) • This method works up to 300,000 light years! Beyond that, the stars in the HR diagram are too faint to be measured accurately.  • Beyond that scale, only ad hoc methods of measuring distances are known (e.g. relying on supernovae measurements, which are of the few events that can still be detected at such distances).  • These measurements have led to accurate maps of the universe at very large scales, which have led in turn to many discoveries of very large-scale structures which would not have been possible without such good astronomy (the Great Wall, Great Attractor, etc.) • Climbing this rung of the ladder (i.e. mapping the universe at its very large scales) is still a very active area in astronomy today!  • Thanks to Charisse Scott for graphics and Powerpoint formatting. Dostları ilə paylaş:

Verilənlər bazası müəlliflik hüququ ilə müdafiə olunur ©genderi.org 2019
rəhbərliyinə müraciət Ana səhifə