Astronomy: 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.