Fundamentals of Astronomy and Celestial Modeling

Astronomy: The scientific study of celestial objects (planets, stars, black holes, etc.) using the scientific method, physics, and mathematics.
Astrology: A pseudoscience assuming supernatural connections between celestial positions and human affairs. It lacks scientific evidence and cannot make accurate predictions.
Historical Shift: Before the telescope, they were practiced together. Post-1600s, Galileo Galilei's observations established astronomy as an independent science.
Precession: The earth's rotational axis wobbles in a circular path every $26,000$ years due to gravitational pulls from the Moon and Sun. This shift (currently $\sim 36^{\circ}$ since 600 BC) means traditional Zodiac signs no longer align with current solar positions.

Axial Tilt: Earth's axis is tilted $23.5^{\circ}$ relative to its orbital plane, which is the sole cause of seasons.
Ecliptic: The apparent annual path of the Sun across the sky.
Seasonal Positions: Vernal Equinox (Spring), Summer Solstice (max Sun height), Autumnal Equinox (halfway downward), and Winter Solstice (min Sun height).
Zodiac: A circle divided into $12$ sections of $30^{\circ}$ each, corresponding to constellations the Sun passes through.

Eratosthenes: First to calculate Earth's circumference ( $\sim 40,000\,km$ ) using the angle of shadows between Syene and Alexandria on the summer solstice.
Heliocentric Model: Copernicus proposed a Sun-centered model; Galileo provided telescopic proof via Jupiter's moons (Io, Europa, Callisto, Ganymede) and the phases of Venus.
William Herschel: Created the first map of the Milky Way, identifying its disk-like distribution.
Edwin Hubble: Proved Andromeda was a separate galaxy using Cepheid variable stars and established Hubble's Law (the universe is expanding).
General Relativity (Einstein): Describes gravity as the curvature of space-time caused by mass. Effects include light bending (gravitational lensing), time dilation (time slows near mass), and length contraction.
Black Holes: Extreme cases where space-time curvature becomes infinite at a singularity.

Wave Structure: Light is an electromagnetic wave consisting of perpendicular electric and magnetic fields.
Speed of Light ( $c$ ): A constant $3 \times 10^8\,m/s$ in a vacuum.
Wave Equation: $c = \lambda \times f$ (where $\lambda$ is wavelength and $f$ is frequency).
Electromagnetic Spectrum: Ranked from low to high frequency: Radio, Microwaves, Infrared, Visible, Ultraviolet, X-rays, and Gamma rays.
Interactions: * Refraction: Light changing direction when entering a new medium. * Reflection: Light bouncing off a surface. * Absorption: Light energy taken in by atoms, creating dark lines in a spectrum used by spectrometers to identify chemical compositions (e.g., Calcium, Hydrogen, Sodium).
Time Machine Effect: Due to light's finite speed, looking at distant objects is looking back in time (e.g., Sun = $8$ minutes ago, Andromeda = $2.5$ million years ago).

Distance Units: * Astronomical Unit (AU): Average Earth-Sun distance ( $149,597,981\,km$ ). * Light Year (LY): Distance light travels in one year ( $9.468 \times 10^{12}\,km$ ). * Parsec (PC): $3.26\,LY$ ; distance where $1\,AU$ subtends an angle of $1$ arcsecond.
Luminosity and Brightness: * Luminosity ( $L$ ): Energy released per second ( $\text{Watts}$ ). * Inverse Square Law: $B = \frac{L}{4\pi d^2}$ . If distance doubles, brightness decreases by factor of $4$ .
Magnitude Scale: * Apparent ( $m$ ): Brightness as seen from Earth. * Absolute ( $M$ ): Brightness if the star were at $10\,pc$ . * Scale Logic: Lower/negative numbers are brighter. A difference of $5$ magnitudes equals a $100$ -fold brightness difference.
Calculations: * Stellar Parallax: $d = \frac{1}{p}$ . * Distance Modulus: $m - M = 5\log(d) - 5$ .

Definition: Two stars gravitationally bound and orbiting each other.
Light Curves: Graphs of brightness vs. time used to detect binary systems and exoplanets. * Primary Minimum: Hotter star is eclipsed. * Secondary Minimum: Cooler star is eclipsed.
Influencing Factors: Orbital period, inclination, star size/shape (tidal distortion), and hot spots from mass transfer.

Refracting Telescopes: Use lenses to converge light. Limited by chromatic aberration and weight.
Reflecting Telescopes: Use mirrors (Newtonian, Cassegrain, etc.). Preferred for large-scale research because mirrors can be supported from behind.
Aperture: The diameter of the objective lens/mirror; the most critical factor for light-gathering and resolution.
Magnification ( $M$ ): Calculated as $M = \frac{F_{objective}}{F_{eyepiece}}$ .
Mounts: * Altazimuth: Simple up-down/side-to-side motion; cannot track Earth's rotation. * Equatorial: Aligned with Earth's axis to track celestial objects indefinitely using motorized drives.