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Solar and sidereal days

Space and time · level 4, lesson 2 of 6

A question to start

The Earth turns once against the stars in 23 hours 56 minutes. So why is a day 24 hours?

The idea

There are two ways to measure a day:

  • A sidereal day is one full turn, measured against the far-off stars.
  • A solar day is from noon to noon, measured against the Sun.

They differ because the planet moves along its orbit while it turns. After one full turn, the Sun is no longer in quite the same direction, so the planet has to turn a little more to bring the Sun back overhead.

The extra bit is about one turn's worth spread over a whole year. Earth goes round the Sun in about 365 days, so each day it needs about \(\frac{1}{365}\) of a turn more: about 4 minutes. Mars takes about 669 sols to go round, so its extra bit is about \(\frac{1}{669}\) of a turn: about 2 minutes.

Mars Earth
Sidereal day (one turn) 24 h 37 min 23 s 23 h 56 min 4 s
Solar day (noon to noon) 24 h 39 min 35 s 24 h
Difference about 2 min 13 s about 3 min 56 s
faces the Sunone turn later:not yet facing itthe Sun

Worked examples

1. Earth's extra bit. A day is 1,440 minutes. \(1{,}440 \div 365 \approx 3.9\) minutes, about 4.

2. Mars's extra bit. A sol is about 1,480 minutes. \(1{,}480 \div 669 \approx 2.2\) minutes, about 2 minutes 13 seconds.

3. Turning backwards. Venus spins very slowly, the opposite way to its orbit. Its solar day is about 117 Earth days, much shorter than its 243-day turn. The rule still holds: what counts is how the turn and the orbit add up.

Try it

  1. What is the difference between a sidereal day and a solar day?
  2. Why is Earth's solar day about 4 minutes longer than its sidereal day?
  3. Which planet's solar day is longer than its sidereal day by less: Mars or Earth? Why?
  4. A planet takes 100 of its own days to go round its star. About what fraction of a turn longer is its solar day?
Answers
  1. A sidereal day is one turn against the stars; a solar day is noon to noon.
  2. Earth moves along its orbit as it turns, so it has to turn about \(\frac{1}{365}\) of a turn more to face the Sun.
  3. Mars: its year has more days in it, so the extra bit each day is a smaller share.
  4. About \(\frac{1}{100}\) of a turn.

Common mistake

"Mars turns once in 24 hours 39 minutes." It turns once in 24 hours 37 minutes. The extra 2 minutes come from its trip round the Sun.

Where it leads