Fundamental Principles of Astronomy and Solar Physics

The Scientific Method and Celestial Motion

In the Scientific Method, a hypothesis must be both testable and falsifiable. When observing the heavens, sidereal measurements are relative to the stars, while synodic measurements are relative to the Sun; for instance, the Moon is full every synodic month.

Kepler's Laws of Planetary Motion

• Kepler's 1st Law: Orbits are ellipses with two foci; the Sun is at one focus. A higher eccentricity (e) indicates a more elliptical orbit.
• Kepler's 2nd Law: The Law of Equal Areas.
• Kepler's 3rd Law: P² = a³, where P is the period in years and a is the semi-major axis in AU.

The Solar System Rotation Curve is defined by the formula v = sqrt(GM/r), where v is orbital velocity and r is the distance from the Sun.

Newtonian Physics and Universal Gravitation

• Newton's 1st Law: Inertia.
• Newton's 2nd Law: F = ma.
• Gravity: F = Gm₁m₂/r².

Two objects orbit a common center of mass, with the smaller object acting as the satellite. Circles and ellipses are bound orbits. Once the velocity reaches escape velocity (v_esc), the orbit becomes unbound (parabolic or hyperbolic if v >> v_esc). The circular velocity is v_circ = sqrt(GM/r), while v_esc = sqrt(2) * v_circ, with G = 6.67e-11.

Tidal Forces and the Roche Limit

Tidal forces cause tides; the tidal bulge points slightly ahead of the Moon due to Earth's rotation, resulting in two high and two low tides each day. The Moon slows Earth's rotation, and Earth accelerates the Moon's orbit due to this bulge. The Roche limit is the point where tidal forces destabilize objects.

Light, Spectroscopy, and Radiation Laws

Light travels at 3e8 m/s in a vacuum. The relationship between properties is wavelength = speed / frequency.

• Emission: An electron emits a photon and drops to a lower energy level (E_photon = ΔE_electron).
• Absorption: The opposite process of emission.
• Spectra: Each atom has a unique emission spectrum.

Luminosity is the total light leaving a source; hotter objects are more luminous. Dense objects emit a blackbody spectrum (continuous). Hotter objects emit more light, more energy, and shorter wavelength light.

• Flux: F = σT⁴, where σ is the Stefan-Boltzmann constant (5.67e-8).
• Wien's Law: Peak blackbody wavelength = 2,900,000 nm * K / T.
• Brightness: Light arriving at a point, B = L / (4πd²), which decreases with the square of the distance.

Telescopes and Observational Techniques

Refracting telescopes use an objective lens to refract light. The aperture is the size of the objective lens, and the focal length is the distance from the lens to the focal plane. Refractors can suffer from chromatic aberration. Reflecting telescopes use primary and secondary mirrors, where the primary mirror is the largest.

Resolution is the smallest detail that can be separated, set by diffraction. The diffraction limit is determined by the ratio of wavelength to aperture. One arcsecond is 1/3600 of a degree. Astronomical Seeing is the limit caused by the atmosphere, which is correctable by adaptive optics. Because the atmosphere blocks certain wavelengths, we use satellites. Interferometric arrays increase resolution by combining multiple telescopes.

Stellar Characteristics and the H-R Diagram

Depth perception relies on stereoscopic vision. Parallax is the only direct way to measure distance; a parsec is the distance of an object with one arcsecond of parallax (parallax = 1 / distance). Surface temperature is found from color using the peak blackbody wavelength formula. Spectral types are categorized from hottest to coolest as O, B, A, F, G, K, M.

Binary systems help determine mass: visual binaries can be seen directly, spectroscopic binaries are detected via Doppler shifts, and eclipsing binaries are identified by dips in total light intensity. The Hertzsprung-Russell (H-R) Diagram shows that most stars are Main Sequence; white dwarfs are below the main sequence, while giants and supergiants are above.

Apparent magnitude (m) is brightness as seen from Earth, while absolute magnitude (M) is brightness at 10 parsecs. The distance modulus is m - M.

The Sun: Structure and Solar Phenomena

The Sun maintains hydrostatic equilibrium, where radiative pressure equals gravity and energy production equals radiated energy. Density, temperature, and pressure increase toward the center. Fusion (hydrogen burning) occurs via the proton-proton chain, slamming four hydrogen nuclei together to create one helium nucleus, energy, positrons, and neutrinos.

Solar Structure

• Core: Where fusion takes place.
• Radiative Zone: Energy moves via radiative transfer.
• Convective Zone: Hot gas rises and cold gas falls.
• Photosphere: The apparent surface where light is emitted and the absorption spectrum is generated.
• Chromosphere: A layer with higher temperatures than the photosphere.
• Corona: Even hotter but very low density; visible during eclipses, emits X-rays, and is very large.
• Solar Wind: Flow of charged particles from coronal holes.

Solar Activity

Sunspots are cooler areas caused by magnetic fields, featuring a dark inner umbra and a cooler penumbra. The Sun follows an 11-year sunspot cycle. Prominences are rising gases in the chromosphere contained by magnetic fields. Solar flares and Coronal Mass Ejections (CMEs) are highly energetic eruptions from sunspot locations. The heliosphere is the extent of the Sun's influence, and helioseismology is used to study inner layers.