Physics · Ch 6 — Gravitation
Interesting Astronomical Facts
Interesting Astronomical Facts
Four short case studies showing how simple photography, geometry, and careful nighttime observation reveal genuine facts about the Earth and the Moon.
1. Measuring Earth's shadow using a lunar eclipse. During a total lunar eclipse (such as the one on 31 January 2018, visible from Tamil Nadu), the Moon passes through Earth's dark inner shadow, the umbra (Figure 6.31), and appears reddish; as it exits the umbra it appears as a crescent. Photographing the eclipse lets you measure the apparent radius of Earth's umbra shadow at the Moon's distance () and the Moon's own apparent radius () directly off the photograph. Their ratio, , combined with the Moon's known true radius (), gives the umbra's true radius as -- close to the correct value of (about error), remarkable given the simplicity of the method. This same style of reasoning -- looking at the curved shape of Earth's shadow falling on the Moon -- is how early astronomers first proved the Earth is spherical.
2. Why don't we get an eclipse every single month? If the Moon's orbital plane exactly coincided with Earth's orbital plane around the Sun, every full Moon would bring a lunar eclipse and every new Moon a solar eclipse. In reality the Moon's orbit is tilted by about relative to Earth's orbital plane, so the Sun, Earth and Moon only line up closely enough for an eclipse during certain specific periods of the year, not every month.
3. Why does the Earth have seasons? A common misconception is that seasons are caused by the Earth's varying distance from the Sun (closer = summer, farther = winter). The real cause is Earth's axial tilt: because the rotation axis stays pointed in a fixed direction in space as Earth orbits the Sun, the Northern Hemisphere leans toward the Sun for part of the year (giving it summer while the Southern Hemisphere, tilted away, has winter) and leans away from the Sun half an orbit later (reversing the seasons). …
What this figure shows. The Sun, Earth and Moon are drawn in a line, with the Earth casting a long cone-shaped shadow away from the Sun. The darkest, fully-shadowed inner cone is labelled the umbra, and it is surrounded by a lighter, partially-shadowed outer cone labelled the penumbra. The Moon's orbit is shown passing through both regions, and the Moon itself is drawn sitting inside the umbra, which is the condition f …
What this figure shows. A schematic of the Earth's umbra shadow (a widening dark cone) with the Moon shown passing through it partway along its orbit; the radius of the umbra disc at the Moon's distance is marked R_s, and the Moon's own radius is marked alongside it, R_m -- these two radii, both measured directly off eclipse photographs as apparent sizes, are compared as a ratio to work out the true size of Earth's shadow at the Mo …
What this figure shows. The Earth is drawn at four positions around its orbit of the Sun, with its rotation axis drawn tilted at a fixed 23.5 degrees to the orbital plane and always pointing in the same direction in space. The diagram shows that because of this fixed tilt, the northern hemisphere leans toward the Sun at one point in the orbit (giving it summer while the southern hemisphere has winter) and leans away from the Sun half an orbit later (reversing the seasons) -- the changing distance to the Sun …
What this figure shows. A long-exposure-style star trail diagram centred on a fixed point labelled the pole star, with every other star's path traced as a curved arc circling around it over the course of a night. The diagram explains that this apparent circular sweep of the whole night sky is not the stars actually moving -- it is the Earth itself spinning about its own axis (which happens to point almost exactly at the pole star), so the star trails are direct photographic proof of E …