4.1 Introduction
47
using GMT or a standard GMT time-zone-related offset. Best practice in astronomy
is not to use daylight saving time. If you need to note down time in your notes, make
sure that you use GMT or your local equivalent.
4.2 Solar Time
Johannes Kepler was a seventeenth-century astronomer and astrologer (at the time,
the two were indistinguishable) born in Weil der Stadt, a town in what is now southern
Germany. He worked for some time with Tycho Brahe, one of the greatest observational astronomers of the time. Tycho was a colourful character who lost his nose in
a duel over a mathematical problem (both sides turned out to be incorrect), had a pet
elk, which died when it fell down a set of stairs whilst drunk, was one of the richest
people in Europe, and died under suspicious circumstances, possibly poisoned by
his assistant over a woman. Claims that he died when his bladder burst when he
refused to leave a banquet in order to relieve himself are likely to be untrue. Kepler
used Tycho’s excellent observations of the motion of the planets to formulate his
famous three laws of planetary motion. It wasn’t until after Kepler’s death that Newton’s three laws and his law of universal gravitation led to a theoretically grounded
understanding of the phenomena described by Kepler’s laws.
Kepler stated in his three laws that each planet orbits the Sun in an ellipse, with
the Sun at one of the foci; that a line drawn between the Sun and the planet will
sweep out equal areas in equal times; and that the square of the orbital period of the
planet around the Sun is proportional to the cube of the semimajor axis of its orbit.
At this point, you may be wondering what this has to do with time. If we measured,
over the course of a year, the time at which the Sun passes through the line drawn
from the northern cardinal point, over the observer’s head, to the south cardinal
point, the meridian, we find that it is not the same every day. Some days, it will
occur before noon on our clock, sometimes after; and on four days, it will be close
to the same time. The variation is between plus fifteen and minus fifteen minutes.
This difference between the time as measured by your watch, mean solar time, and
the time indicated by the Sun, apparent solar time, and the translation between the
two is known as the equation of time (see Fig. 4.1).
There are two reasons for the difference between mean solar time and apparent
solar time. Firstly, let us consider Kepler’s first and second laws. The first law tells
us that for half the year, the distance between the Earth and the Sun decreases until
Earth reaches its closest approach, perigee, occurring in January. It then increases
until reaching maximum distance apogee in June. From the second law, we know
that the Earth must be moving faster in its orbit, the closer it is to the Sun. Hence, the
Earth will travel a greater angular distance around the Sun in a day at perigee than at
apogee, resulting in the Sun moving slightly ahead of the mean. Likewise, because
the Earth is slightly closer to the Sun during perigee than at apogee (and the amount
is very small, only 1.6%), the apparent movement of the Sun caused by the Earth’s
orbit is larger.
47
using GMT or a standard GMT time-zone-related offset. Best practice in astronomy
is not to use daylight saving time. If you need to note down time in your notes, make
sure that you use GMT or your local equivalent.
4.2 Solar Time
Johannes Kepler was a seventeenth-century astronomer and astrologer (at the time,
the two were indistinguishable) born in Weil der Stadt, a town in what is now southern
Germany. He worked for some time with Tycho Brahe, one of the greatest observational astronomers of the time. Tycho was a colourful character who lost his nose in
a duel over a mathematical problem (both sides turned out to be incorrect), had a pet
elk, which died when it fell down a set of stairs whilst drunk, was one of the richest
people in Europe, and died under suspicious circumstances, possibly poisoned by
his assistant over a woman. Claims that he died when his bladder burst when he
refused to leave a banquet in order to relieve himself are likely to be untrue. Kepler
used Tycho’s excellent observations of the motion of the planets to formulate his
famous three laws of planetary motion. It wasn’t until after Kepler’s death that Newton’s three laws and his law of universal gravitation led to a theoretically grounded
understanding of the phenomena described by Kepler’s laws.
Kepler stated in his three laws that each planet orbits the Sun in an ellipse, with
the Sun at one of the foci; that a line drawn between the Sun and the planet will
sweep out equal areas in equal times; and that the square of the orbital period of the
planet around the Sun is proportional to the cube of the semimajor axis of its orbit.
At this point, you may be wondering what this has to do with time. If we measured,
over the course of a year, the time at which the Sun passes through the line drawn
from the northern cardinal point, over the observer’s head, to the south cardinal
point, the meridian, we find that it is not the same every day. Some days, it will
occur before noon on our clock, sometimes after; and on four days, it will be close
to the same time. The variation is between plus fifteen and minus fifteen minutes.
This difference between the time as measured by your watch, mean solar time, and
the time indicated by the Sun, apparent solar time, and the translation between the
two is known as the equation of time (see Fig. 4.1).
There are two reasons for the difference between mean solar time and apparent
solar time. Firstly, let us consider Kepler’s first and second laws. The first law tells
us that for half the year, the distance between the Earth and the Sun decreases until
Earth reaches its closest approach, perigee, occurring in January. It then increases
until reaching maximum distance apogee in June. From the second law, we know
that the Earth must be moving faster in its orbit, the closer it is to the Sun. Hence, the
Earth will travel a greater angular distance around the Sun in a day at perigee than at
apogee, resulting in the Sun moving slightly ahead of the mean. Likewise, because
the Earth is slightly closer to the Sun during perigee than at apogee (and the amount
is very small, only 1.6%), the apparent movement of the Sun caused by the Earth’s
orbit is larger.