Astronomy 217


Prof. Andrew W. Steiner

Aug. 30, 2021

TA James Ternullo

Last Time

  • Solar time
  • Universal time and time zones
  • Sidereal and synodic periods
  • Seasons and leap days
  • Precession of the equinoxes
  • Epochs and stellar motion


  • Phases of the Moon
  • Eclipses
  • Radius of the Earth
  • Parallax
  • Retrograde
  • Telescopes
  • Solar Orbits
  • Python

Phases of the Moon

  • Show that the solar system is 3D
  • Understood from antiquity as due to the reflected light from the sun


  • Solar and lunar eclipses
  • Show that the moon is closer to the sun that the Earth
  • Also do not occur every month because of mismatch between Moon's orbit around Earth and Earth's orbit around sun

Radius of the Earth

  • By measuring the sun’s angle on the Solstice at Alexandria and Syene (on the Tropic of Cancer), Eratosthenes calculated the distance from Alexandria to Syrene was 1/50 of the circumference of the Earth.


  • Diurnal or geocentric parallax: the Earth’s rotation provides a distance measurement, with a baseline of 6371 km $$ \begin{eqnarray} &6371 \mathrm{km} / \tan (0.5^{\circ}) =& \\ &730,044~\mathrm{km} = .005~\mathrm{AU}& \end{eqnarray} $$
  • Annual or heliocentric parallax: the Earth’s orbit provides a another opportunity for distance measurement, with a baseline of \( 1.5 \times 10^{8}~\mathrm{km} \) $$ \begin{eqnarray} &1.5 \times 10^{8}~\mathrm{km} / \tan (0.5^{\circ}) =& \\ & 1.7 \times 10^{10}~\mathrm{km} 114~\mathrm{AU} = & \\ & 1/1800~\mathrm{parsec} & \end{eqnarray} $$

Early Solar System Models

  • Two-dimensional models
  • Models based on perfect circles
  • Geocentric models: did not easily explain retrograde motion
  • Heliocentrism: known to the Greeks and revived in the 16th century by Copernicus

Retrograde Motion

  • Heliocentric models with elliptical orbits provided a simple explanation of retrograde motion


  • Galilean telescopes use one convergent and one divergent lens to produce an upgright image but a narrow field of view
  • Keplerian telescopes use two convergent lenses to give a broad field of view but an inverted image
  • Newtonian telescopes use mirrors and avoid both problems

Moons of Jupiter

  • Galileo discovered the moons of Jupiter in 1610
  • Io, Europa, Ganymede, and Callisto
  • Later that year, it was discovered that Venus has phases just lie the moon
  • Strong support for heliocentric model

Orbits Around the Sun

  • At conjunction, a planet disappears into the Sun. At opposition, a planet is directly opposite the Sun.
  • Inferior \( \Rightarrow \) Orbital Radius < Earth
  • Superior \( \Rightarrow \) Orbital Radius > Earth
  • Inferior planets have one conjunction on the near side of the sun (inferior) and one on the far side (superior).
  • Superior planets have one conjunction, on the far side of the sun, and opposition on the near side

Orbits Around the Sun II

  • To place a planet on its orbit, we specify the angle from the Sun, the elongation (θ).
  • Inferior planets have a Superior planets are in maximum elongation, the Quadrature when their Greatest (western/eastern) elongation is 90° East or Elongation.