The Solar System & the Universe

Orbits and eccentricity

Planets orbit the Sun in ellipses with the Sun at one focus (Kepler's first law). How stretched-out an ellipse is gets measured by its eccentricity:

eccentricity = distance between the foci ÷ length of the major axis

A perfect circle has e = 0; a long, thin ellipse approaches e = 1. Most planetary orbits are nearly circular — Earth's is about 0.017. Example: if the foci are 4 cm apart and the major axis is 10 cm, then e = 4 ÷ 10 = 0.4.

Moon phases

The Moon doesn't make its own light — we see the half lit by the Sun. As the Moon orbits Earth (about every 29.5 days), the lit fraction we see changes: new → waxing crescent → first quarter → waxing gibbous → full → waning gibbous → last quarter → waning crescent. A new moon sits between Earth and Sun (dark side toward us); a full moon is opposite the Sun.

Eclipses and tides

• Solar eclipse: the Moon passes between the Sun and Earth (only possible at new moon), casting a shadow on Earth.
• Lunar eclipse: Earth passes between the Sun and Moon (only at full moon), and Earth's shadow falls on the Moon.
• Tides: the Moon's gravity (and the Sun's) raises bulges of ocean water. The highest "spring" tides happen at new and full moon when Sun and Moon align.

The expanding universe

Light from distant galaxies is shifted toward the red end of the spectrum — a red shift — which means those galaxies are moving away from us, and the farther they are, the faster they recede. This is the main evidence for an expanding universe and the Big Bang theory: everything began about 13.8 billion years ago from an extremely hot, dense state.

Stars themselves are classified by color and temperature — blue stars are hottest, red stars are coolest.