Astronomy — ASTR 1350-850 cheat sheet · Bennett 9e · Kriegler · UNomaha Summer 2026
Scale & cosmic address
Earth → Solar System → Milky Way → Local Group → Local Supercluster → Observable Universe.
AU ≈ 150 M km (Earth–Sun). ly ≈ 10 trillion km. pc = 3.26 ly. c = 300,000 km/s.
Light-time: Moon 1 s · Sun 8 min · Sirius 8 yr · Andromeda 2.5 Myr.
~10²² stars (10¹¹ × 10¹¹). Universe age ≈ 13.8 Gyr.
Sky basics
- 88 IAU constellations (1930). Stars in one may be at very different distances.
- Celestial sphere; ecliptic = Sun's annual path. Milky Way band = edge-on disk.
- Zenith overhead · horizon 90° from zenith · meridian through N–zenith–S.
- 1° = 60' = 3,600". 1 h RA = 15°. Full Moon ≈ 0.5°. Fist at arm's length ≈ 10°.
- Stars rise E, set W (Earth rotates W→E). Circumpolar = never sets.
- Altitude of celestial pole = your latitude (Polaris 41° up ⇒ Omaha).
- Solar day 24 h vs sidereal day 23 h 56 min (Earth has moved ~1° in orbit).
Seasons
- Cause: 23.5° axis tilt, NOT distance (varies only 3%).
- Axis points to Polaris all year; orientation to Sun changes.
- Summer solstice ~Jun 21 (high Sun, 15 h day @40°N). Winter solstice ~Dec 21 (low, 9 h).
- Equinox ~Mar 20 / Sept 22 — Sun rises due E, day ≈ night.
- Precession 26,000 yr (tilt stays 23.5°; "north star" changes).
Moon & eclipses
- Synchronous rotation → always same face toward Earth (no permanent dark side).
- 29.5-day synodic cycle: new → wax cresc → 1Q → wax gib → full → wan gib → 3Q → wan cresc.
- Waxing = afternoon/evening, rises later. Waning = morning, sets later.
- Lunar eclipse at FULL (Earth's shadow on Moon). Solar at NEW (Moon's shadow on Earth).
- 5° tilt of Moon's orbit ⇒ need node alignment too. ~2 eclipse seasons/yr. Saros cycle 18 yr 11⅓ d.
Planets & retrograde
- Naked-eye: Mercury (twilight), Venus (very bright AM/PM), Mars (red), Jupiter (bright), Saturn.
- Apparent retrograde: Earth (inner, faster) laps an outer planet → planet appears to drift backward against stars. Trivial in heliocentric, hard in geocentric.
- Greeks rejected heliocentrism because they couldn't see stellar parallax (stars are far enough that parallax is unmeasurable to the naked eye).
History of astronomy
| Person | Contribution |
|---|
| Eratosthenes (240 BC) | Earth's circumference ≈ 42,000 km |
| Aristotle / Plato | Geocentric, perfect circles |
| Ptolemy (~140 AD) | Most sophisticated geocentric: deferent + epicycle + equant. Lasted 1,500 yr. |
| Copernicus (1543) | Sun-centered model (still used circles → not more accurate) |
| Tycho Brahe | Best pre-telescope data, ~1 arcmin precision |
| Kepler | 3 laws — ellipses (1), equal areas (2), p² = a³ (3) |
| Galileo | Phases of Venus, moons of Jupiter, sunspots, lunar craters, Milky Way stars |
| Newton | 3 laws of motion + universal gravity F = GM₁M₂/r² |
Kepler's laws
- Orbits are ellipses with Sun at one focus.
- Equal areas in equal times (faster near perihelion). Conservation of angular momentum.
- p² = a³ (p in yr, a in AU). Newton form: p² = 4π²a³ / G(M₁+M₂) — lets us "weigh" the central body.
3 hallmarks of science
- Natural causes only (no divine).
- Test models, prefer simpler (Occam's razor).
- Predictions must be falsifiable.
Theory ≠ guess. Theory = explains many obs, big evidence base, hasn't failed crucial tests.
Newton's 3 laws
- Inertia — velocity constant unless net force acts.
- F = m·a (or F = Δp/Δt).
- Equal and opposite forces.
Mass vs weight
Mass (kg) = matter, invariant. Weight (N) = local gravity force = m·g. On Moon weight is ~1/6 (g = 1.6 m/s²) but mass unchanged. Astronauts in orbit are in free fall = weightless but Earth's gravity still ~89%.
Energy
- KE = ½mv². Thermal = avg microscopic KE.
- Radiative = light. PE: gravitational + mass-energy.
- E = mc² — tiny mass deficits → huge energy (fusion in Sun).
- Conservation: momentum, angular momentum, energy.
Gravity
F = G·M₁·M₂ / r². Inverse-square: 2× distance → 1/4 force; 3× → 1/9.
G = 6.674 × 10⁻¹¹ N·m²/kg² (gravity is intrinsically very weak).
Escape speed from Earth ~11.2 km/s.
Tides
- Cause = differential gravity across Earth (∝ 1/r³ — steeper than gravity).
- 2 bulges (near + far side of Moon) ⇒ 2 high tides/day.
- Spring tides at new + full Moon (Sun + Moon align — biggest range).
- Neap tides at quarter Moons (Sun ⟂ Moon — smallest).
- Tidal friction slows Earth ~1.7 ms/century; Moon recedes ~3.8 cm/yr.
Test format reminder
5 tests, best 4 of 5 count (lowest drop). Each = 100 pts, 50 Q multiple choice/matching/T-F. ~45 Q come straight off the Canvas review sheet, 5 from book/online. 60-min window. Each test open Sun→Wed at 11:59 PM. Test 1 = Ch 1–4.