Essential Astronomy Principles & Celestial Mechanics

Fundamental Astronomy Concepts

Angular Measurements & Units

1 degree = 60 arcminutes = 3600 arcseconds; 1 radian = 180/π degrees; 1 light year =

Understanding Angular Diameter

Angular diameter (or size) is the angle an object subtends, measured in units like degrees, arcminutes, radians, or arcseconds. The angular size of an object (α) is calculated as: α = D (diameter) / d (distance), where D and d must be in the same units.

Celestial Sphere & Earth's Motion

Circumpolar Stars & Polaris

Circumpolar stars are stars that appear to never set because they closely circle a celestial pole, such as Polaris (the North Star). The altitude of a celestial pole above the horizon is equal to your latitude.

• At 40° North latitude, the North Celestial Pole (and Polaris) will be 40° above the horizon.
• At the Equator (0° latitude), Polaris will be on the horizon.
• At the North Pole (90° latitude), Polaris will be directly overhead (at the zenith).

Seasonal changes are more extreme at higher latitudes.

Earth's Axial Tilt & Seasons

Summer Solstice (June 21)

• The Northern Hemisphere receives the most direct sunlight, resulting in the longest day of the year.
• The sun takes its highest path in the sky, rising and setting at its most extreme north of east.
• The sun remains below the horizon all day south of the Antarctic Circle.
• The sun remains above the horizon all day north of the Arctic Circle.
• The sun is directly overhead the Tropic of Cancer (23.5° North).

Winter Solstice (December 21)

• The sun takes its lowest path in the sky, rising and setting at its most extreme south of east.
• The sun is directly overhead the Tropic of Capricorn (23.5° South).

Equinoxes (March 21 & September 22)

• The sun rises precisely east and sets precisely west.
• There are equal hours of daylight and night across the globe.
• The sun shines directly overhead on the Equator at noon.

Key Latitudes & Circles

• North Pole: 90°N
• Arctic Circle: 66.5°N (23.5° South of the North Pole)
• Equator: 0°
• Antarctic Circle: 66.5°S (23.5° North of the South Pole)
• South Pole: 90°S

Celestial Phenomena: Eclipses

Johannes Kepler formulated three fundamental laws describing planetary motion around the Sun:

• Kepler's First Law: Elliptical Orbits

  The orbit of each planet around the Sun is an ellipse, with the Sun located at one of the two foci.

• Kepler's Second Law: Equal Areas in Equal Times

  As a planet moves around its orbit, an imaginary line connecting the planet to the Sun sweeps out equal areas in equal intervals of time. This implies that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.

• Kepler's Third Law: Orbital Period & Distance

  More distant planets orbit the Sun at slower average speeds. This relationship is described by the formula p² = a³, where 'p' is the orbital period in years and 'a' is the average distance from the Sun in Astronomical Units (AU). This law applies specifically to orbits around our Sun.

Basic Physics Principles

• Speed: The rate at which an object covers distance (e.g., m/s), without regard to direction.
• Velocity: Speed with a specified direction.
• You are weightless when in a state of free fall.
• Newton's Second Law (F=ma): Force equals mass times acceleration. Knowing the acceleration (e.g., Earth's gravity), one can measure force to solve for mass.