Declination, obliquity, and all that

Definitions, etymology and values of parameters and terminology related to orbits.

Introduction

This post defines astronomical terms like ecliptic, declination, and synodic. tbl-em is a cheat sheet of orbital and rotational parameter terminology with values for the Earth and Moon. Section 3 provides some definitions and word etymology.

Definitions and Parameter Values

Table 1: Orbital and Rotational Parameters for the Earth and Moon

Parameter	Symbol	Definition	Earth Value	Moon Value
Ecliptic inclination	i	Tilt of orbital plane relative to a reference plane	23.44°	5.145°
Inclination to lunar equator		Angle between rotational axis and orbital axis		1.543°
Axial tilt or Obliquity		Angle between rotational axis and orbital axis	23.44°	6.68°
Declination range		Max angular distance from celestial equator	±23.44°	±28.6° (Earth + Moon tilt)
Orbital eccentricity	e	Deviation of orbit from a perfect circle	0.0167	0.0549
Orbital period (sidereal)	T	Time to orbit relative to stars	365.256 days	27.3217 days
Rotation period (sidereal)		Time to spin once relative to the stars	23h 56m 4s	27.3217 days (locked)
Synodic rotation period		Time between identical phase positions	24h	29.5306 days
Orbital semi-major axis	a	Average Earth–orbited distance (mean)		384,400 km
Orbital/nodal procession		Rotation of the Moon’s orbital plane around Earth		18.6 years
Apsidal procession		Rotation of the Moon’s elliptical orbit (perigee/apogee advance)		~8.85 years
Lunar libration		Apparent wobble allowing >50% of surface to be seen		±7–8° in angle
Lunar standstill cycle		Maximal swing in declination due to nodal procession		18.6 years
Escape velocity		Velocity to escape gravity from surface	11.2 km/s	2.38 km/s
Orbital speed (mean)		Average speed in orbit	29.78 km/s	1.022 km/s
Mass	M		\(5.97 \times 10^{24}\) kg	\(7.35 \times 10^{22}\) kg
Diameter	D		12,742 km	3,474 km
Surface gravity	g		9.81 m/s²	1.62 m/s²
Perigee		Closest point in elliptical orbit	147.1 million km (Sun)	363,300 km (Earth)
Apogee		Farthest point in elliptical orbit	152.1 million km (Sun)	405,500 km (Earth)

Moon verified against Wikipedia

https://en.wikipedia.org/wiki/Orbit_of_the_Moon#/media/File:Lunar_perturbation.jpg

Terminology

ecliptic

The apparent annual path of the Sun across the sky, which corresponds to the plane of Earth’s orbit around the Sun.
Etymology: From Latin ecliptica (linea) “(line) of eclipses,” because eclipses occur when the Moon crosses this path.

obliquity

The angle between an object’s rotational axis and the perpendicular to its orbital plane; for Earth, this is 23.44°.
Etymology: From Latin obliquitas, from obliquus meaning “slanting” or “not straight.”

synodic

Relating to the time between successive conjunctions of a celestial object with the Sun as seen from Earth; for the Moon, ~29.53 days.
Etymology: From Greek synodikos, from synodos “meeting, conjunction,” from syn- (“together”) + hodos (“way, journey”).

apsidal

Pertaining to an apsis, a point of closest (perigee) or farthest (apogee) approach in an elliptical orbit.
Etymology: From Latin apsis, from Greek hapsis “loop” or “arch.”

libration

A perceived oscillation or “wobble” of the Moon, allowing observers from Earth to see slightly more than half of its surface over time.
Etymology: From Latin libratio, from librare “to balance,” from libra “scales, balance.”

perigee

The point in the orbit of the Moon (or any satellite) at which it is closest to Earth.
Etymology: From Greek peri- “near” + ge “Earth.”

apogee

The point in the orbit of the Moon (or any satellite) at which it is farthest from Earth.
Etymology: From Greek apo- “away from” + ge “Earth.”

celestial equator

An imaginary great circle in the sky that lies in the same plane as the Earth’s equator. It serves as a fundamental reference line for the equatorial coordinate system used by astronomers to locate objects in the sky

ascending node, descending node

Point where the moon’s orbit crosses the ecliptic plan

Gibbous

Latin gibbosus = humped, hunched