Tycho and Kepler (52 page)

Stjerneborg (“Star Castle”), the partly subterranean observatory Tycho built in the 1580s outside the perimeter wall of Uraniborg to accommodate some of his largest and most powerful instruments.

The Chapel of the Magi at Roskilde Cathedral, with tombs of Frederick II and his father, as it appears today. It was this chapel that Tycho neglected to keep in good repair, thus incurring the wrath of the teenage Christian IV.

King Christian IV of Denmark, whose birth horoscope Tycho drew up, and who later became Tycho’s nemesis, in a portrait by Pieter Isaacsz.

Wedding medallion portraits (1597) of Johannes Kepler and his first wife, Barbara.

Emperor Rudolph II of the Holy Roman Empire, the eccentric, reclusive patron of both Tycho and Kepler, in a portrait by Hans von Aachen.

The cliff-top
Benatky Castle, northeast of Prague, that Emperor Rudolph gave to Tycho to create a second Uraniborg. The mural depicting hunting scenes and featuring the emperor is visible on its walls.

Drawing by an unknown artist depicting riots between Archduke Leopold’s troops and Protestant vigilantes in the streets of Prague, near the Keplers’ home, in February 1611.

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PPENDIX
1

ANGULAR DISTANCE

A simple way to approach the definitions of the terms
angular distance, angle of separation
, and
degree of arc
is to imagine oneself at the center of a giant clock face, where the two hands meet. From that point of view, the angle of separation or angular distance between an object at “twelve o’clock” and an object at “one o’clock” is thirty degrees of arc.
Likewise the angular distance between “one o’clock” and “two o’clock,” and so forth. The angular distance between an object at “twelve o’clock” and another at “two o’clock” is sixty degrees of arc, and so forth. The entire circle has 360 degrees. To understand the concept roughly with regard to the sky, draw an imaginary line between two stars directly overhead whose angle of separation you want
to measure and let that line continue all the way around you and the earth beneath your feet until it comes up the other side of the sky and joins its other end, so that the line has drawn a huge circle all the way around the celestial sphere. That huge circle is the equivalent of the clock face, and you are in the center where the two hands meet. If the two stars look to be at, let us say, one and
two o’clock, then their angular separation is thirty degrees.

Because celestial objects that interest astronomers are often closer together than one degree of arc, degrees are divided into smaller segments. There are sixty minutes of arc in one degree of arc; sixty seconds of arc or arcseconds in one minute of arc.

Two objects whose angle of separation is, let us say, thirty degrees of
arc (from twelve to one on the clock face as viewed from the center of the clock) can actually be either quite close to one another or very far apart. For example, looking from the window of my study, I see two trees whose distance from one another (if you go out
and
measure it) is about twelve feet. Their angular separation from where I stand is about thirty degrees. Beyond them is the sky. Lining
up each tree with a star, those two stars also have an angular separation from one another of about thirty degrees when viewed from my study. However, those two stars are definitely not just twelve feet apart. Knowing what angle separates two objects does not tell us the
distance
between them.

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PPENDIX
2

VOCABULARY OF ASTRONOMY

Much of the vocabulary that is essential to understanding this book is explained in the relevant chapters, but here are a few more useful terms:

Meridian circle:
Starting at the north celestial pole, draw an imaginary line to the zenith above where you are standing, then continue the line around the celestial sphere until you have brought it all
the way around the celestial sphere, through the south celestial pole, to meet its tail again at the north celestial pole. What you have drawn is a line of longitude or a meridian, the celestial equivalent of the lines of longitude or meridians to be found on a globe of Earth. This meridian is perpendicular to the horizon.

Altitude
is the distance of a star or planet above the horizon, measured
in degrees. A complete circle is 360 degrees, so the altitude of a star at the zenith is 90 degrees. No star can ever have an altitude greater than 90 degrees.

Azimuth
is the distance of an object from the meridian, also measured in degrees. Imagine again drawing the meridian hoop. Stand facing north and imagine that line. If you see a star off to the left or right of that line, that star
is not on your meridian. Its azimuth is the measurement of how far it is from the meridian.

Meridian, altitude, and azimuth—like horizon and zenith—are dependent on where an observer is standing.

Astronomers need measurements that will not change with the position of the observer—measurements that stay put, as do the celestial equator and the celestial poles. An astronomer in Denmark must
be able to tell an astronomer in Italy what
the
position of a star or planet is without using Denmark as a reference point. Hence another set of terms:

The
prescribed meridian
is the meridian line established not by the position of the observer but by the position of the Sun at the vernal equinox.

The
declination
of a celestial object is its distance in degrees above the celestial equator.

Right ascension
is its distance in degrees east of the prescribed meridian.

Declination and right ascension are hence independent of the observer’s position on Earth. Whether you are in New York or Arizona or Turkey, the declination and right ascension of a particular star will be the same.

Two more measurements are related not to the horizon or the celestial equator but to the ecliptic:

The
latitude
of a celestial body is how many degrees it is above or below the ecliptic.

Longitude
is a body’s position
along
the ecliptic, measured in degrees eastward from the vernal equinox.

It is useful to remember all these terms in groups of four:

Altitude
and
azimuth
are measurements related to the
horizon
and the
meridian
.

Declination
and
right ascension
are measurements
related to the
celestial equator
and the
prescribed meridian
.

Latitude
and
longitude
are measurements related to the
ecliptic
and the
vernal equinox
.

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PPENDIX
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KEPLER’S USE OF TYCHO’S OBSERVATIONS OF MARS TO FIND THE ORBIT OF EARTH

To discover what Earth’s motion was like, Kepler put himself and the readers of
Astronomia Nova
in the position of a Martian astronomer observing Earth.

The Martian begins the series of observations when Mars is on Earth’s apsidal line (that is, the line running through the Sun, the center of Earth’s
orbit, Earth, and Earth’s positions at aphelion and perihelion—
see figure 19.1
). Every 687 Earth-days after that (687 Earth-days is one Martian year), the Martian takes another observation of Earth. Each time, Mars has completed an orbit and returned to Earth’s apsidal line. To put himself and his readers in the place of that Martian observer, Kepler reversed the direction along which Tycho had
observed Mars from Earth, in effect allowing himself to watch Earth from a stationary Mars.