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Coordinate Transforms. z. x. y. Equatorial and Cartesian Coordinates. declination (δ). Equator. right ascension (α). Equatorial and Cartesian Coordinates. x = Rcosα y = Rsinα. y. α. R. x. right ascension (α). y. declination (δ). z. r = 1. δ. R = rcosδ z = rsinδ. R.

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equatorial and cartesian coordinates

z

x

y

Equatorial and Cartesian Coordinates

declination (δ)

Equator

right ascension (α)

equatorial and cartesian coordinates1
Equatorial and Cartesian Coordinates

x = Rcosαy = Rsinα

y

α

R

x

rightascension (α)

y

declination (δ)

z

r = 1

δ

R = rcosδz = rsinδ

R

precession
Precession
  • Because the Earth is not a perfect sphere, it wobbles as it spins around its axis
  • This effect is known as precession
  • In the last lecture, I noted that the equatorial coordinate system relied on the idea that the Earth rotated such that only α, and not δ, was a time-dependent coordinate
the effects of precession
The effects of Precession
  • Currently, the star Polaris is the North Star (it lies roughly above the Earth’sNorth Pole at δ = 90oN)
  • But, over the course ofabout 26,000 years avariety of different pointsin the sky will truly beat δ = 90oN
  • The declination coordinateis time-dependent albeiton very long timescales
  • A precise astronomicalcoordinate system must account for this effect
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