Two Systems of Stellar Coordinates

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Stellar Coordinates Just as we use a map of the Earth to find different locations, we can use a map of the sky to find stars and other objects. Every place on Earth has a pair of coordinates to identify it and every point on the celestial sphere has a pair of coordinates too. There are two systems for this: Azimuth and Altitude and Right Ascension and Declination. Azimuth and Altitude Azimuth and altitude are probably how you would point out a star to someone. Azimuth is the angle around the horizon from due north and corresponds to the points on a compass. An azimuth of 0 degrees is due North, 90 degrees is due East, 180 degrees is due South, and 270 is due West. Altitude is the height of the star, in degrees above the horizon. Altitude can range from 0 degrees (on the horizon) to 90 degrees (directly overhead). The drawback to this system is that as a star rises and sets, its position in the sky relative to the due north and its height change. This means that the azimuth and altitude change throughout the night and that observers at two different locations could see the same star at different azimuth altitude coordinates. (Why? Because the reference plane, the astronomical horizon, which is understood to intersect the celestial sphere as a great circle, changes—relative to the fixed stars—as the earth rotates and is different from different positions on earth.) Right Ascension and Declination Right ascension and declination are similar to longitude and latitude. The lines similar to the longitude lines on a globe are called Right Ascension. Right ascension is measured around the celestial equator towards the east. This angle is measured in hours, minutes, and seconds. A full rotation of 360 degrees is 24 hours, so each hour of right ascension is about 15 degrees along the celestial equator. The 0 reference meridian is that which passes through the vernal equinoctial point. Declination is similar to latitude and measures how far above or below the celestial equator an object is. On object below the celestial equator has a negative declination; an object on the celestial equator has a declination of zero. An object with a right ascension of 0 hours and declination of 0 degrees lies at the vernal equinoctial point. Since the Right Ascension and Declination are relative to fixed stars, these coordinates do not change over time or with the position of the observer. (This last claim requires some qualification: the position of the vernal equinoctial point does change, relative to the fixed stars, due to precession of the equinoxes; so does the position of the celestial north pole, relative to the fixed stars.) .

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Equatorial and Cartesian Coordinates • Consider the Unit Sphere (“Unit”: I.E
Coordinate Transforms Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. declination the distance from the center of the (δ) sphere to its surface is r = 1) • Then the equatorial coordinates Equator can be transformed into Cartesian coordinates: right ascension (α) – x = cos(α) cos(δ) – y = sin(α) cos(δ) z x – z = sin(δ) y • It can be much easier to use Cartesian coordinates for some manipulations of geometry in the sky Equatorial and Cartesian Coordinates • Consider the unit sphere (“unit”: i.e. the distance y x = Rcosα from the center of the y = Rsinα α R sphere to its surface is r = 1) x Right • Then the equatorial Ascension (α) coordinates can be transformed into Cartesian coordinates: declination (δ) – x = cos(α)cos(δ) z r = 1 – y = sin(α)cos(δ) δ R = rcosδ R – z = sin(δ) z = rsinδ Precession • Because the Earth is not a perfect sphere, it wobbles as it spins around its axis • This effect is known as precession • The equatorial coordinate system relies on the idea that the Earth rotates such that only Right Ascension, and not declination, is a time-dependent coordinate The effects of Precession • Currently, the star Polaris is the North Star (it lies roughly above the Earth’s North Pole at δ = 90oN) • But, over the course of about 26,000 years a variety of different points in the sky will truly be at δ = 90oN • The declination coordinate is time-dependent albeit on very long timescales • A precise astronomical coordinate system must account for this effect Equatorial coordinates and equinoxes • To account
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