Knowing the RA/DEC of a star how do I locate a star from ground?

Question

Standing in Melbourne at 4 am in the morning on 14th April 2019, Sirus RA = 06h 45m 08.9s, Dec = -16° 42' 58"..How do I Locate this. Standing facing east I turn myself towards south approx 90 Deg and then look up about 16 Deg, I do not find any star.

Answer 1

Calculating local sidereal time exactly is not trivial as shown by the calculation for local sidereal time given at Approximate Sidereal Time:

The Greenwich mean sidereal time in hours is: $$GMST = 6.697374558 + 0.06570982441908 D_0 + 1.00273790935 H + 0.000026 T^2$$ where $T = D/36525$ is the number of centuries since the year 2000.

Fortunately thereare a number of online calculators that will do that for you.

You can, however ballpark it knowing that at the equinox in March (~21st, depending on the year, because you also need to take leap years into account), local sidereal time is 12 hours different than local time (without daylight saving). i.e. 6 pm (18:00) is 06:00 LST. This means that RA 06h00m is overhead at 18:00 local time.

Then add 1 hour for each $\frac{1}{2}$ month or 2 hours for each month since then. So, mid-April is about 1 month after the March equinox which means that RA 08h00m is overhead at 18:00 local time, and mid-May will be 2 months so RA 10h00m is overhead at 18:00.

From there, it is just like a clock - midnight is 6 hours later than 18:00 so you add 6 hours to the local sidereal time calculated earlier meaning that in mid-April RA 14h00m is overhead at midnight.

What this tells us is that around the March equinox (~21st), Sirius (RA 06h45m) is overhead at about 18:45, which we can round off to around 19:00 (7 pm) given the roughness of the calculation so far. We can guess then that it will set then around 6 hours later, at about 1 am.

In mid-April, RA 21h00m will be overhead at around 19:00 (7 pm), which means Sirius will have been overhead about 2 hours earlier - around 17:00 (5 pm), which means it will set around 11 pm, and in mid-May will set around 9 pm.

Melbourne is located at ~145° E, ~38° S. From this you can work out the relative angle from the declination (Sirius dec. is -16°43'). Melbourne is at 38° south, so declination -38 is directly overhead. Sirius is at dec. -16°43' (so about -17°) so it will be about 20° north of directly overhead.

So, you would face towards north and look upwards almost to directly overhead. Knowing the LST, you know the RA that is directly overhead and can count towards the west (or east, depending on the month), and knowing that in mid-April Sirius was overhead at around 5 pm and will set around 11 pm, you can find it.

NB. James K's answer is really worth reading.

Answer 2

You know that stars seem to move in the sky because the Earth is rotating. The RA and Dec tell you the position of the star relative to other stars. But because the Earth is rotating, the RA and Dec don't tell you where to look in the sky.

In general, you need to know two more pieces of information: where you are standing on Earth and the time. It is then possible to calculate the position in the sky. This position is sometimes called the Alt(itude) (angle above horizon) and Az(imuth) (bearing from North). See for example Software to convert RA and DEC into ALT and AZ

The calculations basically involve spherical trigonometry, so are too difficult for most people to do in their head.

But rather than try to do this yourself, it is better to get some planetarium software, such as Stellarium. This shows you what the sky looks like at any given time and where stars and planets can be seen.

If you prefer a coding solution, you can use astropy, or pyephem. Libraries also exist for other languages. Search for "Ephemeris" and the name of your favourite language.

Even better is to learn your way around the sky, by recognising bright constellations and asterisms. You find Sirus by first finding Orion, and then extending the line of his belt to the west, and there you will see a surprisingly bright star, Sirius.

However, you won't see Sirus at 4 am in Melbourne since it will have already set.