Solar time and sidereal time

A solar day is measured from one noon to the next — that is, by the Sun. A sidereal day is one true 360° rotation, measured by timing a star from meridian to meridian.

• Mean solar day = 24 h 00 min 00 s (by definition of our clocks).
• Sidereal day = 23 h 56 min 04 s — about 4 minutes shorter.

Why the difference? In one day the Earth also travels about 1° around the Sun. After a full 360° spin, the star is back on the meridian — but the Earth must turn about 1° more to bring the Sun back to the meridian. That extra 1° takes roughly 4 minutes.

The practical result: any given star rises about 4 minutes earlier each night, which is 2 hours earlier after a month and a full 24 h after a year — so the same constellations return at the same time each year.

Your turn — the drifting stars

Why is the sidereal day shorter?

Apparent time, mean time and the equation of time

Real ("apparent") solar days are not all the same length, for two reasons:

• The Earth's orbit is an ellipse, so the Earth moves faster near perihelion and slower near aphelion (Kepler's 2nd law).
• The Earth's axis is tilted, so the Sun's daily motion is not parallel to the celestial equator.

So we invent a fictitious mean Sun that moves at a perfectly constant rate, and set our clocks by it. The difference between the two is the equation of time:

Where you see it: a sundial shows apparent solar time. To get clock time you must apply the equation of time (and add an hour in British Summer Time). Plotting the Sun's position at clock-noon through the year traces a figure-of-eight called the analemma.

Longitude, GMT and time zones

Because the Earth turns 360° in 24 hours, longitude and time are the same thing:

• GMT / UT — the mean solar time at the Greenwich meridian (0°), the world's time standard.
• Time zones — bands roughly 15° wide, so clocks within a zone all read the same, avoiding a different time in every town.
• BST — British Summer Time: clocks are put forward 1 hour from GMT in the summer half of the year.

Local mean time vs zone time: the UK spans about 10° of longitude, so the Sun really crosses the meridian in Norwich (1.3° E) about 22 minutes earlier than in Plymouth (4.1° W) — even though the clocks agree.

Your turn — local time

Sunrise first

The year and the leap-year rules

The tropical year — the time from one vernal equinox to the next, which is what the seasons follow — is 365.2422 days. A calendar of whole days must fix that awkward 0.2422.

• Julian calendar (46 BC): a leap day every 4 years → an average year of 365.25 days. That is 11 minutes too long, which built up to about 10 days of error by the 16th century.
• Gregorian calendar (1582, adopted in Britain in 1752): a leap year every 4 years, except century years, unless they divide by 400.

How accurate? 365.2425 vs the true 365.2422 — an error of only about 0.0003 days a year, or one day in roughly 3000 years.

Your turn — counting leap years

Which kind of time?

Tap a statement, then tap where it belongs.

Match the description to the term

Tap a description on the left, then its matching term on the right.

Reading a sundial

Is it a leap year?

Precession: the slow wobble

The Earth is not a perfect sphere, and the pull of the Sun and Moon on its equatorial bulge makes the axis wobble slowly, like a spinning top. The axis traces out a cone once every 25 800 years (about 26 000). This is precession.

• The pole star changes. Polaris is our pole star now; around 3000 BC it was Thuban (in Draco), and in about 12 000 years it will be Vega.
• The vernal equinox drifts westwards along the ecliptic — which is why the zodiac "signs" of ancient astrology no longer line up with the constellations the Sun is actually in.
• Because RA and dec are measured from the vernal equinox, star catalogues must quote an epoch (for example J2000.0) and be updated.

Do not confuse: the tilt angle stays at about 23.5° — precession changes the direction the axis points, not how far it leans.

The changing pole star

The big ideas to know

That is Time & the Calendar covered for Edexcel GCSE Astronomy. Press Finish to see your score.