Forest Ho-Chen '22
The Celestial Sphere
Astronomy studies celestial objects and phenomena. When doing astronomy, we want ways to state the location of celestial objects through coordinates. The way we usually do this is by projecting the sky onto a large sphere centered around the viewer. This is an imaginary sphere called the Celestial Sphere. If we want to talk about the distances on this sphere, we can do this by measuring the angles. This is like a three-dimensional version of the polar coordinate system in two dimensions.
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First, a few definitions. Assuming the observer is always upright and normal (perpendicular) to the surface of the Earth, the point directly above the observer is called the zenith, and the point directly below the observer is the nadir. The plane perpendicular to the line from the zenith and the nadir is called the horizon. The horizon is not the same as the surface of the Earth because the Earth is round and approximately spherical (lunar eclipses and sunsets are a thing, and matter can’t go faster than the speed of light), while the horizon is a plane.
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The celestial sphere will appear to rotate over time, caused by the Earth rotating around its axis. This leads to the North and South celestial poles, which are the projection of the Earth’s North and South poles onto the celestial sphere. The plane perpendicular to this axis is the celestial equator, and the plane passing through the celestial poles, the zenith, and the nadir is the meridian. The meridian intersects the horizon at the North and South points (labeled N and S), while the celestial equator intersects the horizon at the East and West points (labeled E and W).
Here are two ways of stating the location of celestial objects through coordinates. The first way is the Horizontal Coordinate System, which uses the coordinates of altitude and azimuth. Altitude is the vertical angular distance from the horizon to the object. Sometimes, the zenith distance, which is the complement of the altitude, is used to denote the angular distance from the zenith to the object. Azimuth has multiple ways to measure. One way (used here) is to look from the zenith down to the horizon and measure the angle to the object by going clockwise from the North point. Other systems may go clockwise from the South point instead. The Horizontal Coordinate System is dependent on the latitude of the observer, but the longitude of the observer is not as important.
A very important trick to know about the Horizontal Coordinate System is that the altitude of the celestial pole is equal to your latitude. For example, Yardley and Newtown are at a latitude of about 40.2 degrees North. This means that to point a telescope at the North celestial pole, we should point it directly North (azimuth of zero) and raise the altitude to about 40.2 degrees.
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Another celestial coordinate system is the Equatorial Coordinate System. Unlike the Horizontal Coordinate System, the Equatorial Coordinate System does not depend on the position of the observer on Earth. Instead of using altitude and azimuth as the coordinates, the Equatorial Coordinates use Declination and Right Ascension. Declination is similar to latitude, while Right Ascension is similar to longitude. A very important trick to know about the Equatorial Coordinate System is that the declination of your zenith is equal to your latitude. So the Declination of a star at our zenith would be approximately 40.2 degrees.
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Right Ascension is a bit more complicated. The Earth revolves around the Sun, and the Earth is spinning, so it appears that the Sun rises and sets. With this, we can get that if we tracked the position of the Sun with an observer always looking at it, the Sun will follow a curve in the sky known as the Ecliptic. The Ecliptic is slanted to the tilt of the Earth of about 23.5 degrees. The Ecliptic intersects the Celestial Equator at two points, the Vernal and Autumnal Equinoxes (labeled VE and AE). The Vernal Equinox is usually around March 20th, and the Autumnal Equinox is usually around September 21st. (For 2021, it was on 9/22 at 3:20 PM GS Solar Time). At the Vernal Equinox, the Declination of the Sun goes from negative to positive, and at the Autumnal Equinox, it goes from positive to negative.
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With the Earth revolving around the Sun but also spinning around its axis, the time relative to the Sun will be different from the time relative to other stars. This leads to the difference between Solar and Sidereal Time. At the Vernal Equinox, we state that it is zero Sidereal Time, corresponding to Zero Hours Right Ascension. As time passes, we will have Solar Days and Sidereal Days, with the difference being that Sidereal Days are about 4 minutes shorter than Solar Days, about 1/365th of a day. This means that stars will appear earlier as time progresses.
After some time, we see a star in the sky on the meridian between the North Celestial Pole and the South Point, and the star’s Right Ascension will be equal to the current Sidereal time. This is how Right Ascension is measured. When combined with Declination, we can get the coordinates of every point on the Celestial sphere, regardless of the location of the observer on the Earth.