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

Today

• Phases of the Moon
• Eclipses
• Parallax
• 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

Eclipses

• 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

• 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.

Parallax

• 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

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

Telescopes

• 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.