# PHY115: Professional Skills in Physics and Astronomy

Positional Astronomy: Session 2

Solar Time

Using sidereal time to run your daily affairs would be pretty inconvenient. We saw that the relationship

LST = HAx + RAx

holds for any celestial object, including the Sun. So the local sidereal time is also given by

LST = HA + RA,

where HA and RA are the hour angle and right ascension of the Sun. But of course, the Sun moves around the ecliptic, so RA changes through the year. If we had to go to work every day at the same local sidereal time, sometimes this would be in the day, and sometimes at night!

It's hardly surprising then, that we use solar time to govern civil timekeeping. The solar time is related to the hour angle of the sun, so that the Sun is always near the observer's meridian at noon. By convention, local noon is at 12:00, so that the solar time is given by

ST = HA + 12h.

The 12 hour correction ensures that the solar time is always 12:00 when the Sun is on the meridian.

In reality, things are a little more complicated than described above, as the Earth's orbit is elliptical, which means that the length of the solar day varies throughout the year. This means that the Sun might be up to 15 minutes in front or behind the meridian at local noon. We won't go into that in this course, but it is discussed in more detail in Vik Dhillon's excellent notes from the discontinued PHY105.

Universal Time

The hour angle of the Sun depends on the observer's longitude and so solar time is different for observers at different longitudes. It is convenient to define a reference longitude to use for setting clocks by. This reference point is the Royal Observatory at Greenwich, the same point used to define the zero of the longitude scale. We can then define Greenwich Mean Time (GMT), or Universal Time (UT), with reference to the hour angle of the Sun for an observer at Greenwich (HA☉,G) as

UT = GMT = HA☉,G + 12h.
Sidereal Time & Solar Time

Quite often we will want to convert between sidereal time and solar time (either local or GMT). For example, we may wish to know if a certain star transits during the day or not. This is quite easy, given the relationships presented here, provided one knows the right ascension of the Sun on any given day. You can roughly calculate the Sun's right ascension from it's motion around the ecliptic, or (if you want a precise value), use the online calculator from the US Department of Energy.

For a given LST, the hour angle of the Sun is simply given by

HA = LST - RA.

And the local solar time is just

ST = HA + 12h.

Converting from local solar time to UT is just as easy. The relationship between local time and UT is clearly a function of longitude, as the local solar time at Greenwich is the same as UT. Since the Earth rotates 15° in one hour, we have,

ST = UT ± l/15,

where l is the longitude of the observer. The plus sign is used when the longitude is to the east, and the minus sign when the longitude is to the west.

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