Lecture 7 - Angular Diameter and Lunar Eclipses (1/29/96)

Seeds: Chapter 3

  1. Eclipses and Shadows
    • Sun is only source of light in solar system
    • Blocking of Sun by one body in front of another -> Eclipses
    • Eclipses are just shadows
    • Shadows for extended light sources are "fuzzy"
    • Fuzzy outer region where source is partially blocked = penumbra
    • Dark inner shadow where source is completely blocked = umbra
    • Lunar Eclipses
      • 1st contact: leading edge of Earth touches Sun, partiality starts
      • 2nd contact: leading edge of Earth covers Sun, totality starts
      • 3rd contact: trailing edge of Earth uncovers Sun, totality ends
      • 4th contact: trailing edge of Earth uncovers Sun, eclipse ends
      • Partial and Annular Eclipses
      • Refraction of Sunlight in Earth's atmosphere: red moon at totality
      • The Line of Nodes and Eclipse Seasons
    • Angular Diameters and the Small-Angle Formula
      • Definition of Angular Diameter
      • The Small Angle Formula: Arc of a Circle
      • The Small Angle Formula: Triginometry
      • Example: the diameter of the Moon
    • The Aberration of Starlight and the Earth's Motion
      • Like rain seems to slant toward us when we run into it
      • Speed of Earth / Speed of Light = 1 / 10^4
      • Aberration angle = 20.6"
      • Aberration on sky, little circles

Next Lecture - Solar Eclipses and Early Greek Astronomy

Eclipses and Shadows

The shadow cast by an opaque screen in front of a point-like light source is always sharp. However, the shadow cast by a body eclipsing an extended light source like the Sun is "fuzzy". There is a region surrounding the dark inner shadow that is not as dark - from those points looking back toward the light the screen only partly covers the light. This is called the penumbra, and is distinguished from the dark inner shadow, or umbra.

Experiment: try looking at the shadow of your hand on a wall on a sunny day.

Shadows

The umbra of the Earth is a cone that extends 1.4 x 10^6 km anti-sunward. The Moon's orbit intersects this 27% of the way along, and at this point the umbra is around 2.7 times the Moon's diameter in cross-section.

The umbra of the Moon extends only around 383000 km, compared to its distance from the Earth of 384000 km. Only when the Moon is at perigee and is closest to the Earth in its elliptical orbit can a total solar eclipse occur. If it is more distant, the umbra falls short of the Earth's surface and the Moon is smaller than the Sun in angular size. During a full eclipse the Sun is seen in a ring or annulus around the edge of the Moon --- thus this is know as an annular eclipse.

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Steven T. Myers - Last revised 03May96