Geodesy of the Terrestrial Planets

Earth rotates from West to East, known as "Prograde" rotation.
The Sun, Moon, and stars rise in the East and set in the West.
Earth rotation: 360° / 24 hours = 15° / hour.
Satellites in Low-Earth Orbit (LEO) have an orbital period of approximately 90 minutes.
In 90 minutes, Earth rotates 22.5°, causing the satellite track to shift westward by 22.5° with each orbit.
Sidereal day (stellar day): 23h 56m 4.1s
Synodic day (solar day): 24h 00m

Sidereal period: Time for a planet or satellite to return to the same state (rotation or position) relative to the stellar reference frame.
Synodic period: Time for a planet or satellite to return to the same state relative to an observer.
Synodic rotational period: Time between successive recurrences of the same phase with respect to the Sun (e.g., full moon to full moon).
Synodic orbital period: Time for two planets to return to the same geometric configuration as they orbit the Sun.

For prograde orbits, synodic periods are longer than sidereal periods; the opposite is true for retrograde orbits.
Prograde Rotation Case: \frac{T{syn}}{T{sid}} = \frac{T{syn}}{T{orb}} + 1 => \frac{1}{T{orb}} - \frac{1}{T{sid}} = \frac{1}{T_{syn}}
Retrograde Rotation Case: \frac{T{syn}}{T{sid}} = \frac{T{syn}}{T{orb}} - 1 => \frac{1}{T{orb}} + \frac{1}{T{sid}} = \frac{1}{T_{syn}}

Synodic rotational period of the Earth:
- Sidereal day: 23h 56m 4.1s
- Synodic day: 24h 00m
- Earth orbital period: T_{orb} = 365.2563604167 days
Synodic period of the Moon:
- Sidereal period: T_{sid} \approx 27.3 days
- Earth orbital period: T_{orb} \approx 365.25 days
- Synodic period: T_{syn} \approx 29.5 days
Time between two Earth/Mars oppositions:
- Earth orbital period: ~1 year
- Mars orbital period: ~1.84 years ≈ 670 days
- Earth/Mars synodic period: ~2.2 Earth years ≈ 800 days

Seasons are caused by the tilt of Earth’s rotational axis (23.4°).
Northern summer coincides with Southern winter, and vice versa.
Equinoxes (Mar 20/21, Sep 22/23): 12-hour daylight everywhere; sub-solar point moves along the Equator.
Northern Solstice (~June 21/22): Long daylight hours in the north, short in the south; Arctic circle in permanent daylight, Antarctic circle in permanent darkness; sub-solar point moves along the Northern Tropic.
Southern Solstice (~Dec 21/22): Long daylight hours in the south, short in the north; Arctic circle in permanent darkness, Antarctic circle in permanent daylight; sub-solar point moves along the Southern Tropic.
Equatorial areas always have 12-hour daylight.
Seasons are not equally long due to Earth’s orbit eccentricity and varying orbital speed.
Northern Hemisphere Season Lengths:
- Spring: 92.75 days
- Summer: 93.65 days
- Fall: 89.85 days
- Winter: 88.99 days