Eclipses, Tides and Precession

Three things at once

You already know how big the Earth, Moon and Sun are and how far apart they sit. This module is about what the three of them DO to each other. Three effects, three different causes: eclipses come from shadows, tides come from gravity, and precession comes from the Earth wobbling on its axis like a slowing spinning top.

The words for a shadow

Every eclipse question turns on two parts of a shadow:

Find the umbra

Sunlight comes from the left and the Earth casts a shadow to the right. Tap the UMBRA, the dark central cone where the Sun would be completely hidden.

The ring of fire

In an annular solar eclipse a ring of sunlight stays visible around the Moon. Why?

• The Moon is near apogee, so its disc looks too small to cover the Sun
• The Moon is too thin at that phase to block the light
• Sunlight bends around the Moon through its atmosphere
• The Moon sits slightly above the line, so the top of the Sun shows

Two different line-ups

The two kinds of eclipse are not variations of one thing. They need the three bodies in a different order, and they happen at opposite phases of the Moon. And they are rare because the Moon's orbit is tilted about 5 degrees, so most months the shadow passes above or below its target. An eclipse needs the Moon near a node, where its tilted orbit crosses the Earth's orbital plane.

A lunar eclipse

Select the TWO statements that are true of a total lunar eclipse.

• It can only happen at full moon
• The Moon passes into the Earth's umbra
• It is visible only from a narrow track on the Earth
• It can only happen at new moon

The four umbral contacts

A total lunar eclipse is timed by four moments as the Moon crosses the Earth's umbra. Put them in the order they happen.

• First contact: the Moon's leading edge touches the umbra
• Second contact: the trailing edge enters, so the Moon is fully inside and totality begins
• Third contact: the leading edge reaches the far side of the umbra, so totality ends
• Fourth contact: the trailing edge leaves the umbra and the eclipse is over

Why two high tides a day

The Moon's gravity pulls hardest on the water nearest to it, and least on the water on the far side. That stretches the oceans into two bulges, one facing the Moon and one opposite it, so most coasts get two high tides and two low tides roughly every day. The Sun does the same thing, but its tidal effect is only about half the Moon's, even though it is far more massive, because it is so much further away.

Match each line-up to what it produces

When are tides largest?

Spring tides happen when the tidal effects of the Sun and Moon add together. When is that?

• At new moon and full moon, when the three bodies are roughly in line
• In the spring, once the season changes
• At first quarter and third quarter
• Only when the Moon is at perigee

The wobbling axis

The Earth's axis stays tilted at about 23.5 degrees, but the direction it points slowly swings round in a circle, like a spinning top slowing down. This is precession:

What precession changes

Select the TWO things that precession changes over thousands of years.

• Which star sits closest to the celestial pole
• Where on the horizon the stars rise and set
• The angle of the Earth's tilt, which grows steadily larger
• The length of a day, which doubles over one cycle

Measured without a telescope

Two Greek astronomers worked out the scale of this system more than 2,000 years before anyone left the Earth. Eratosthenes measured the size of the Earth from two shadows. Aristarchus used the Moon at exactly half phase to compare the distance to the Sun with the distance to the Moon, and timed how long the Moon took to cross the Earth's shadow during a lunar eclipse to compare their sizes. Both used geometry and careful observation, nothing else.

How Eratosthenes measured the Earth

Put the steps of Eratosthenes' method in order.

• Note that at midday on one day of the year, the Sun is directly overhead at Syene and casts no shadow
• At the same moment, measure the angle of the shadow cast by a vertical pillar at Alexandria
• Take that angle as the fraction of a full circle between the two cities, about a fiftieth
• Multiply the known distance between the cities by that fraction to get the whole circumference

Solar and lunar eclipses

A solar eclipse happens at _____ moon, when the Moon's shadow falls on the Earth; a lunar eclipse happens at _____ moon. The dark central shadow is the _____. The largest tidal range, at new and full moon, is called a _____ tide, and the smallest is a _____ tide. The slow swing of the Earth's axis, taking about 25,800 years, is called _____.

Explain it

The Moon goes round the Earth every month, so why do we not get a solar eclipse and a lunar eclipse every single month? Explain in your own words.

• Say what has to line up for each kind of eclipse
• Give the tilt of the Moon's orbit and say what it does to the shadow
• Use the word node, and say what has to be true of the Moon's position
• Finish by saying why total solar eclipses are seen by so few people at a time