6.4 Willem de Sitter
109
consulting his parents, he decided to accept the offer. After passing his doctoral
exam (masters), de Sitter indeed traveled to Cape Town in August 1897. He
was supposed to make photometric observations of stars in the CPD. For this
he had brought a Zöllner photometer (see Fig. 2.6). However, the telescope
he was to work with had not been completed in time. He did make several
observations for Kapteyn’s program, but spent most of his time observing the
four large satellites of Jupiter. This concerned precise measurements of the
positions to study the characteristics of their orbits.
The satellites or moons of Jupiter had been discovered by Galileo Galilei
when he was the first to look at the sky with a telescope (and report on it in
a publication) in 1609 and 1610. Now their orbits were fairly well known,
but there were also mutual attractions that ensured that there was systematics
in these orbits in the form of resonances, so that they circled around Jupiter
in a fixed regularity. The inner three moons (Io, Europa and Ganymede) do
so in orbital periods that have almost exactly the ratio 4 : 2 : 1. Think of a
situation where the inner two satellites pass each other in their orbits. If Io
(who is closest to Jupiter) has gone around twice and has returned to the same
position, Europe also has returned there after one orbital period. If the ratio
between their periods is not exactly 1 : 2—for example if Io at that time would
be slightly ahead of Europa—their mutual attraction will slow down Io a bit
and accelerate Europa somewhat, changing that ratio back closer to the exact
ratio 1 : 2. In this way they get stuck in a stable pattern of mutual perturbations
that returns regularly after one or more orbital periods. 4 This is much more
common in the Solar System, also among the planets; for example, Jupiter
and Saturn are close to a 5 : 2 resonance and the Earth and Venus in a 3 : 8
one. This makes the Planetary System rather robust. In practice, the situation
is more complicated, because Jupiter’s satellites orbit only in approximately
circular orbits around the planet and also in slightly different orbital planes. In
the case of Jupiter there also is a fourth satellite, Callisto, which is in resonance
with Ganymede of 3 : 8.
After his return to the Netherlands in December 1899—he had married
Eleonora Suermondt (1870–1952) in 1898—de Sitter wrote his dissertation
on the subject of the orbits of the Jupiter satellites; he was Kapteyn’s first PhD
student when he obtained his degree in 1901. This issue of the Jupiter satellites
has interested him for the rest his life and he did much work on it until the end.
He became much better known among a wider audience because of his work
on Einstein’s general theory of relativity and their joint publication, which
4 If the satellites were to orbit in pure circles in one plane and if there were only two them, the orbital
times would be in exact resonance, but in the actual situation it will be approximate. A regular pattern is
already sufficient to create and strengthen the orbital resonances in an approximate manner.
109
consulting his parents, he decided to accept the offer. After passing his doctoral
exam (masters), de Sitter indeed traveled to Cape Town in August 1897. He
was supposed to make photometric observations of stars in the CPD. For this
he had brought a Zöllner photometer (see Fig. 2.6). However, the telescope
he was to work with had not been completed in time. He did make several
observations for Kapteyn’s program, but spent most of his time observing the
four large satellites of Jupiter. This concerned precise measurements of the
positions to study the characteristics of their orbits.
The satellites or moons of Jupiter had been discovered by Galileo Galilei
when he was the first to look at the sky with a telescope (and report on it in
a publication) in 1609 and 1610. Now their orbits were fairly well known,
but there were also mutual attractions that ensured that there was systematics
in these orbits in the form of resonances, so that they circled around Jupiter
in a fixed regularity. The inner three moons (Io, Europa and Ganymede) do
so in orbital periods that have almost exactly the ratio 4 : 2 : 1. Think of a
situation where the inner two satellites pass each other in their orbits. If Io
(who is closest to Jupiter) has gone around twice and has returned to the same
position, Europe also has returned there after one orbital period. If the ratio
between their periods is not exactly 1 : 2—for example if Io at that time would
be slightly ahead of Europa—their mutual attraction will slow down Io a bit
and accelerate Europa somewhat, changing that ratio back closer to the exact
ratio 1 : 2. In this way they get stuck in a stable pattern of mutual perturbations
that returns regularly after one or more orbital periods. 4 This is much more
common in the Solar System, also among the planets; for example, Jupiter
and Saturn are close to a 5 : 2 resonance and the Earth and Venus in a 3 : 8
one. This makes the Planetary System rather robust. In practice, the situation
is more complicated, because Jupiter’s satellites orbit only in approximately
circular orbits around the planet and also in slightly different orbital planes. In
the case of Jupiter there also is a fourth satellite, Callisto, which is in resonance
with Ganymede of 3 : 8.
After his return to the Netherlands in December 1899—he had married
Eleonora Suermondt (1870–1952) in 1898—de Sitter wrote his dissertation
on the subject of the orbits of the Jupiter satellites; he was Kapteyn’s first PhD
student when he obtained his degree in 1901. This issue of the Jupiter satellites
has interested him for the rest his life and he did much work on it until the end.
He became much better known among a wider audience because of his work
on Einstein’s general theory of relativity and their joint publication, which
4 If the satellites were to orbit in pure circles in one plane and if there were only two them, the orbital
times would be in exact resonance, but in the actual situation it will be approximate. A regular pattern is
already sufficient to create and strengthen the orbital resonances in an approximate manner.