Sidereal Day
Earth's rotation period measured against the stars, not the Sun.
Formula
Variables
Example
≈ 23 h 56 m 04 s
How it works
A sidereal day is the time Earth takes to rotate once relative to distant stars, which is slightly shorter than a solar day because Earth is also moving along its orbit around the Sun. After one solar day, Earth must rotate a little more than 360° to bring the Sun back to the same position in the sky, but it needs less than 24 hours to realign with the stars. This formula captures that difference by correcting the solar day with the fraction of a year Earth advances in orbit during one day.
When to use it
Use this when converting between the familiar 24-hour solar day and the true rotation period of Earth relative to inertial space. It is especially useful in astronomy, celestial navigation, and problems involving star positions or Earth-rotation timing.
Worked example, step by step
Given: T_sol = 24.00 h T_yr = 365.25 d = 365.25 × 24 = 8766 h Step 1: Compute the ratio T_sol / T_yr T_sol / T_yr = 24 / 8766 ≈ 0.0027379 Step 2: Add 1 to the ratio 1 + T_sol / T_yr ≈ 1.0027379 Step 3: Apply the formula T_sid = T_sol / (1 + T_sol / T_yr) T_sid = 24.00 / 1.0027379 ≈ 23.93447 h Step 4: Convert the decimal part to minutes and seconds 0.93447 h × 60 ≈ 56.068 min 0.068 min × 60 ≈ 4.1 s Final answer: T_sid ≈ 23 h 56 m 04 s
Common mistakes to avoid
- using 365 days instead of 365.25 days, which slightly changes the result
- mixing hours and days in T_yr without converting units consistently
- thinking the sidereal day is longer than the solar day, when it is actually shorter
Did You Know?
A sidereal day is ~4 minutes shorter than a solar day because Earth must turn a little extra to face the Sun again.
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