Altitude and azimuth from the last lesson change every minute and from town to town. A star catalog needs coordinates that stay with the stars. The celestial sphere borrows Earth's own grid: declination is like latitude and right ascension is like longitude.
- Declination ($\delta$): degrees north ($+$) or south ($-$) of the celestial equator, from $+90^\circ$ at the north celestial pole to $-90^\circ$ at the south one. Vega is at $+38.8^\circ$; Sirius at $-16.7^\circ$.
- Right ascension (RA): how far east of a starting line a star is, measured along the celestial equator. The starting line runs through the March equinox, the point where the Sun crosses the celestial equator heading north. RA is counted in hours, minutes and seconds, from $0^{\mathrm{h}}$ to $24^{\mathrm{h}}$.
Why it works
Why hours? The sky turns $360^\circ$ in a day, so splitting the equator into 24 hours means one hour of RA turns past your meridian in one hour of time (sidereal time, see the next lesson). So $24^{\mathrm{h}} = 360^\circ$, $1^{\mathrm{h}} = 15^\circ$, and $1^{\mathrm{m}} = 15' = 0.25^\circ$. A star with RA $2^{\mathrm{h}}$ greater than another crosses your meridian 2 hours after it, every night. Because both coordinates are tied to the stars, not to you, they stay the same as the sky turns and from anywhere on Earth (they creep slowly over centuries as Earth's axis wobbles).
Key idea
Declination is the sky's latitude, in degrees from the celestial equator. Right ascension is the sky's longitude, measured east from the March equinox in hours: $1^{\mathrm{h}} = 15^\circ$. A star passes overhead where your latitude equals its declination.
Worked examples
Worked example: Hours to degrees
Sirius has right ascension $6^{\mathrm{h}}\,45^{\mathrm{m}}$. How many degrees east of the March equinox is that?
- $45^{\mathrm{m}} = \frac{45}{60} = 0.75$ h, so the RA is $6.75$ h.
- $6.75 \times 15^\circ = 101.25^\circ$.
Answer: About $101^\circ$.
Worked example: Overhead where?
Vega has declination $+38.8^\circ$. Where on Earth does it pass straight overhead?
- A star reaches the zenith where the latitude equals its declination.
- So at latitude $38.8^\circ$ N, near Washington, D.C., Vega passes overhead once a day.
Answer: Latitude $38.8^\circ$ N.
Worked example: Which comes first?
Star A has RA $5^{\mathrm{h}}\,30^{\mathrm{m}}$ and star B has RA $9^{\mathrm{h}}$. How long after A does B cross the meridian?
- Stars cross the meridian in order of increasing RA, because the sky turns westward.
- $9 - 5.5 = 3.5$ h of RA, so B crosses about $3.5$ h after A.
Answer: About $3.5$ hours later.
Common mistake
Right ascension hours are not clock times. A star at RA $18^{\mathrm{h}}$ does not rise at 6 pm; it is $270^\circ$ east of the March equinox. The clock time it rises shifts by about 4 minutes every night, so it changes through the year while the RA stays put. Check: if RA were a clock time, the star would rise at the same time all year, but the winter and summer skies are different.
The Sun's RA does work like a clock: on the March equinox the Sun is at RA $0^{\mathrm{h}}$, and it moves about $2^{\mathrm{h}}$ east each month. See which stars are up from your own latitude in the Sky and Solar System lab.