Distances to the Stars
As the seventeenth century wore on, investigations progressed to finding the distances of stars. The distance to a star would now be given in multiples of the radius of Earth’s orbit, or astronomical units. The modern value for one astronomical unit is ≈150 million kilometres (≈93 million miles).
Observations made six months apart from the same observatory are from the opposite ends of a baseline about 300 million kilometres long – long enough to produce a measurable shift in the positions of a handful of stars (heliocentric parallax). These parallaxes are very small and so a new unit of distance was introduced, the parsec. A star one parsec away would show a displacement of one arc second (1/3600th of a degree) over a 150 million km baseline. One parsec is ≈3.26 light years; one light year is ≈9.46 x 1012 km.
Descartes’ claim that the Sun is another star suggested an approach that could give a rough measurement of the distances to the stars. If the stars are assumed to be almost identical then since light reduces with the square of the distance, the relative distance (i.e. in multiples of Earth’s radius) of the Sun to a star can be estimated from their relative brightnesses.
Christiaan Huygens (1629-95) put a screen between himself and the Sun. He then made a tiny hole in the screen and reduced the sunlight coming through the screen by putting a lens in front of the hole until the Sun, viewed through the hole, had the same brightness as Sirius. From this he derived the distance to Sirius as 27,664 astronomical units; today’s value is ≈544,000 astronomical units (≈8.6 light years).
In 1668, James Gregory (1638-75) used a planet as an intermediate. He waited until the planet was equal in brightness to Sirius and then compared the brightness of the planet (light from the Sun reaching us via the planet) with the brightness of the Sun (light reaching us directly from the Sun). He obtained a distance of 83,190 astronomical units to Sirius but he knew that he had used a scale of the Solar System that needed to be revised upwards. Using this method Newton obtained a distance of one million astronomical units to Sirius.
Proper Motion
Following Edmund Halley’s discovery of proper motion in 1718, James Bradley (1693-1762) in 1746 noted that it was necessary to separate proper motion from the apparent motion caused by the moving Solar System carrying Earth with it.
In 1760 Tobias Mayer (1723-62) noted that if we walk in a forest, the trees in front of us appear to open out and those to the rear seem to close together. Similarly, if the Solar System is moving towards a certain point, the solar apex, the stars would appear to move away from this apex in a great circle towards a point in the opposite direction, the solar antapex.
In 1783 William Herschel having studied the proper motions of seven bright stars was able to plot the Sun’s motion through the Galaxy and deduced that the Sun is moving towards a point in the constellation of Hercules. By 1937, from a study of the proper motions of several hundred stars Friedrich Wilhelm August Argelander (1799-1875) obtained a solar apex not far from that proposed by Herschel.
In 1751-3 at the Cape of Good Hope, Nicolas Louis de Lacaille (1713-62) surveyed the southern skies. He discovered twenty-four new nebulae and clusters and charted the positions of nearly 10,000 stars. In 1847 Thomas Galloway (1796-1851) analysed the proper motions of eighty-one of these and obtained an apex position that matched the position derived from the northern stars.
Barnard’s Star has the largest proper motion of any star known. Discovered in 1916 by Edward Emerson Barnard (1857-1923) it is the third closest star to the Sun, 6 light years away and moving across the sky at 10.31 arc seconds (about 1/200th of the Moon’s angular diameter) each year.
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