Sidereal versus solar day calculator
A solar day is longer than a sidereal one because the planet has moved along its orbit and must turn a little further to face the Sun again.
hours
days
Solar day length
23.999 997hours
- Longer than the sidereal day by
- 3.932 minutes
- Solar days per orbit
- 365.256 40
- Sidereal days per orbit
- 366.256 40
- Solar day in days
- 0.999 999 89
Show the working
- Sidereal rotation period = 23.9345
- Orbital period = 365.256
- sidereal_days = 23.9345 / 24 = 0.997 27
- Solar day in days = 365.256 != 0.997 27 ? 1 / (1/0.997 27 - 1/365.256) : 0 = 1
- Solar day length = 1 * 24 = 24
- Longer than the sidereal day by = (24 - 23.9345) * 60 = 3.931 67
- Solar days per orbit = 1 > 0 ? 365.256 / 1 : 0 = 365.256
- Sidereal days per orbit = 0.997 27 > 0 ? 365.256 / 0.997 27 : 0 = 366.256
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- 1 / solar day = 1 / sidereal day - 1 / orbital period
Earth's sidereal day is 23 h 56 m 4 s. The extra 3 m 56 s is the planet catching up with its own orbital motion.
The relation is why there is exactly one more sidereal day than solar day in a year.
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