Download The Celestial Sphere

The Celestial Globe
Astronomers view the sky (half-hemisphere) available to us above the horizon at
any time, and from a particular location on the earth. In order to understand
where a specific object (e.g. star, planet or galaxy) is, we need a coordinate
system attached to the sky, that emulates the longitude, latitude system on the
earth.
The Earth Coordinate System
Let us review that system on the surface of the earth.
▪ There are great circles of longitude which pass through the N and S poles,
and which are perpendicular to the equator
▪ Those great circles define “time zones”
▪ Rochester is close to 75o W of Greenwich, England or 15h W of Greenwich
England. Evidently 24h = 360o, or 1h = 15o.
▪ Longitude is measured along the Earth’s equator to the great circle of
longitude through the city of interest, measured from the zero-point,
Greenwich.
▪ There are parallels of latitude parallel to the equator, and measured in
degrees (o) N and S of the equator. Note from the figure that they really are
parallel, while the longitude circles are not.
A great circle means that the associated plane passes through the center of the
earth, but the plane associated with the latitude parallels do not. All longitude
circles have the same diameter; the latitude circles do not. A quick aside: you
might like a very interesting book , “Longitude : The True Story of a Lone Genius
Who Solved the Greatest Scientific Problem of His Time” by Dava Sobel
“The thorniest scientific problem of the eighteenth century was how to determine
longitude. Many thousands of lives had been lost at sea over the centuries due to
the inability to determine an east-west position. This is the engrossing story of
the clockmaker, John "Longitude" Harrison, who solved the problem that Newton
and Galileo had failed to conquer, yet claimed only half the promised rich reward.
“
Coordinate System on the Sky
We imagine a similar situation on the sky. The celestial sphere is an imaginary
sphere of infinite radius with the earth located at its center. The north and south
celestial poles of the celestial sphere are aligned with the N and S poles of the
Earth. The celestial equator lies in the same plane as does the Earth's equator.
An astronomer can only see half the sky at a time, that is, only half the sky is
above the horizon at any time. But the sky keeps moving as the earth rotates.
Just as the sun rises and sets every day, so does every star in the sky each
night.
North Celestial Pole (NCP) and the South Celestial Pole (SCP) - these are
just the intersection of the north and south pole axis with the celestial sphere.
Celestial Equator – Extension of the earth's equatorial plane to its intersection
with the celestial sphere
Horizon - The horizon changes relative to the polar axis depending on your
position on earth. It divides the hemisphere that is the sky from the rest of the
celestial sphere. The great circle through the zenith and the NCP intersects the
horizon at the cardinal direction on the earth, N.
Zenith - The point on the celestial sphere directly overhead and 90o away from
the horizon.
Meridian - The line that extends from the north point on the horizon upwards
through the zenith and then downward to the south point on the horizon.
We can locate any object on the celestial sphere by giving it two coordinates,
called the Right Ascension α (analogous to longitude on the Earth) and the
Declination δ (analogous to latitude on the Earth). These are called celestial
coordinates.
Similar to longitude on Earth, the Right Ascension α of an object on the celestial
sphere is measured eastward along the celestial equator, from a zero-point (i.e.
where α = 0o), defined to be the vernal equinox – the place where the Sun is on
the sky on March 21.
Similar to the latitude on Earth, the Declination δ of an object on the celestial
sphere is measured northward or southward from the plane containing the
equator. δ of the equator is 0o, δ of the North Celestial Pole NCP, +90o, and δ of
the South Celestial Pole SCP, -90o.
Stars and galaxies have (almost) fixed positions in α and δ. The Sun and
planets, on the other hand, move among the distant stars so that their
coordinates change throughout the year. Because of the Earth's yearly orbital
motion, the Sun appears to circle the ecliptic, inclined at 23.5o to the celestial
equator. All solar system planets and moons are approximately in the ecliptic
plane. The comets, however, and their close cousins the Kuiper Belt Objects
are more broadly distributed.
Latitude and Longitude System on the Earth
In addition to the fixed celestial coordinate systems on the sky, based on the
earth’s coordinates, there are also ALT-AZ horizon-based coordinate systems.
The problem is, as the sky apparently turns with time, the altitude ALT and the
azimuth AZ change. However, if one knows the sidereal time ST – star time (not
solar time), it is possible to find the fixed sky coordinates.
The altitude ALT is measured in degrees from the horizon.
The azimuth AZ is measured from the N point on the horizon with zero degrees
corresponding to North, and increasing in a clockwise fashion. Thus, 90 degrees
is East, 180 degrees is South, and 270 degrees is West.
Sidereal Time and Hour Angle
Sidereal Time ST is = the right ascension α of a star on the meridian. Thus ST =
0h when the vernal equinox γ (position of Sun on March 21) is on the meridian.
So ST = 0h at noon on March 21, and 12h at noon on September 21.
Hour angle HA is the angular measure in h,m,s from the meridian westward
along the celestial equator to the foot of the hour circle (like longitude circle)
through the object. ST = HA + α
In class and in lab you will have many opportunities to exercise these definitions.
They are important so that we can go to the telescope and begin observations.
Calculators on the web allow you to figure out sidereal time as well as other
things.
http://tycho.usno.navy.mil/sidereal.html (working as of 2016!)
Sidereal Time and Solar Time
Careful observation of the sky will show that any specific star will cross directly
overhead (on the meridian) about four minutes earlier every day. In other words,
the day according to the stars (the sidereal day) is about four minutes shorter
than the day according to the sun (the solar day).
If we measure a day from noon to noon - from when the sun crosses the
meridian (directly overhead) to when the sun crosses the meridian again - we will
find the average solar day is about 24 hours.
If we measure the day according to a particular star - from when that star crosses
the meridian to when that star crosses the meridian again - we will find the
average sidereal day is 23 hours and 56 minutes.
Referring to our previous assertion that ST = 0 on March 21 at noon, ST will be
approximately 0h 4m on March 22, 0h 8m on March 23, and 2h on April 21 at
noon.
The reason for this is illustrated below. On the first day, point A points directly
toward the sun at exactly twelve noon. After a full rotation of the Earth, point A is
pointing in the same direction in space, but since the Earth has also proceeded
along its orbit, point A is no longer facing the sun. It takes another 4 minutes of
rotation for point A to again face the Sun. (The effect is exaggerated in the
figure). And over the course of a year’s time, the sidereal year is 1 day shorter
than a solar year -- [4m/d / (24 x 60m/d)] x 365d/y = 1d/y. So while it is tricky, it
is possible to compute the ST fairly readily.