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3 Astronomy Around 1875
Sun, the distance between them is the smallest (i.e. only one third of the
distance from the Sun to the Earth); that would be a good time to measure
the distance of Mars. This could be done by measuring the exact position of
Mars relative to the stars in the background, from two places on Earth as far
apart as possible. Those positions will be different (the so-called parallactic
effect); the difference depends on how far apart the two measuring points
on Earth are (which distance is known) and on the distance to the Earth of
Mars at that moment. The latter can then be calculated, and with that the
scale of the Solar System is determined. This is usually expressed in the
average distance from the Earth to the Sun, the ‘Astronomical Unit’. This is
149.6 million kilometers. The angle at which the radius of the Earth would
be seen from the Sun is of course also a measure for the distance from the
Earth to the Sun. This angle is called the solar parallax and is 8 .79 (8.79
seconds of arc). In the middle of the nineteenth century this distance was
only known to no better than a few percent.
There is a second method for determining the scale of our Solar System.
For this you can use Venus (but in principle also Mercury). These two
planets can stand between the Earth and the Sun and sometimes cross in
front of the Sun. The exact time at which the planet passes the Sun’s edge
differs for different places on Earth, and can therefore also serve as a basis
for a distance calculation. This method was first applied by Edmond Halley
in 1676, using a transit of Mercury; however, the result was unsatisfactory
because this planet is too far from the Earth. Venus transits provide much
more precise observations, but they are rare. They occur in pairs with an
interval of a few years, but in between those pairs the interval is about
120 years. The transits of 1761 and 1769 had already yielded a reasonable
result. Various places on Earth were visited to observe the following transits
of 1874 and 1882.
These Venus transits were extensively studied by the Canadian-American
astronomer Simon Newcomb (1835–1909), who we will encounter below
in relation to Kapteyn. He determined the solar parallax (and thus also the
Astronomical Unit) to an accuracy of unprecedented 0.2%! In the twentieth
century, the first method (the one with Mars) was successfully replaced by
using asteroids, when some of these were discovered that can come much
closer to the Earth than Mars.
In 1875 there was no understanding of the physical processes in the Sun
that cause it to radiate. Of course it was possible to measure how much
energy was involved. One could also calculate how much energy the Sun
contains in gravitation, i.e. how much energy would be released if the Sun
would contract to a very small size. From this one could deduce how long the
3 Astronomy Around 1875
Sun, the distance between them is the smallest (i.e. only one third of the
distance from the Sun to the Earth); that would be a good time to measure
the distance of Mars. This could be done by measuring the exact position of
Mars relative to the stars in the background, from two places on Earth as far
apart as possible. Those positions will be different (the so-called parallactic
effect); the difference depends on how far apart the two measuring points
on Earth are (which distance is known) and on the distance to the Earth of
Mars at that moment. The latter can then be calculated, and with that the
scale of the Solar System is determined. This is usually expressed in the
average distance from the Earth to the Sun, the ‘Astronomical Unit’. This is
149.6 million kilometers. The angle at which the radius of the Earth would
be seen from the Sun is of course also a measure for the distance from the
Earth to the Sun. This angle is called the solar parallax and is 8 .79 (8.79
seconds of arc). In the middle of the nineteenth century this distance was
only known to no better than a few percent.
There is a second method for determining the scale of our Solar System.
For this you can use Venus (but in principle also Mercury). These two
planets can stand between the Earth and the Sun and sometimes cross in
front of the Sun. The exact time at which the planet passes the Sun’s edge
differs for different places on Earth, and can therefore also serve as a basis
for a distance calculation. This method was first applied by Edmond Halley
in 1676, using a transit of Mercury; however, the result was unsatisfactory
because this planet is too far from the Earth. Venus transits provide much
more precise observations, but they are rare. They occur in pairs with an
interval of a few years, but in between those pairs the interval is about
120 years. The transits of 1761 and 1769 had already yielded a reasonable
result. Various places on Earth were visited to observe the following transits
of 1874 and 1882.
These Venus transits were extensively studied by the Canadian-American
astronomer Simon Newcomb (1835–1909), who we will encounter below
in relation to Kapteyn. He determined the solar parallax (and thus also the
Astronomical Unit) to an accuracy of unprecedented 0.2%! In the twentieth
century, the first method (the one with Mars) was successfully replaced by
using asteroids, when some of these were discovered that can come much
closer to the Earth than Mars.
In 1875 there was no understanding of the physical processes in the Sun
that cause it to radiate. Of course it was possible to measure how much
energy was involved. One could also calculate how much energy the Sun
contains in gravitation, i.e. how much energy would be released if the Sun
would contract to a very small size. From this one could deduce how long the