Motion of the Moon

What time is it in this drawing?

What time is it in this drawing?

What time is it in this drawing?

What time is it in this drawing?

What time is it in this drawing?

What time is it in this drawing?

Lunar eclipse

Discussion What phase must the Moon be in for there to be a lunar eclipse?

Discussion Why don’t we have a lunar eclipse every time there is a full Moon?

Total Lunar eclipse of July 16, 2000

Discussion Why do you think the eclipsed Moon appears red?

Discussion The Moon goes through its phases in 29.53 days. This is called the synodic month, i.e. the month relative to the Sun. The actual orbital period of the Moon is 27.32 days, the sidereal month. Why is there a difference in the synodic and sidereal months?

In the 27.32 days that the Moon has taken to orbit the Earth the Earth has moved in its orbit relative to the Sun. The Earth moves about 1 degree per day so that after 27 days the Moon needs to move through an extra 27 degrees in the sky to get back to the same position relative to the Sun.

Synodic and Sidereal months

Discussion If the Earth moves faster in its orbit does the length of the sidereal month change?

Discussion If the Earth moves faster in its orbit, does the synodic month get longer or shorter?

Discussion The Moon always keeps the same side facing the Earth. Does this mean the Moon does not spin on its axis? Explain?

Synchronous Rotation If the Moon did not spin on its axis we would see the Moon’s entire surface over the month. The Moon therefore does rotate but the rotation period is exactly equal to its orbital period and rotates such that we always see the same face. Thus, the Moon’s rotation period is synchronous with its orbital period.

Discussion What is the length of the sidereal and mean solar days on the Moon?

Mean solar day on the Moon 29.5 Earth days, the Sun rises in the east sets in the west 14.75 days later, followed by 14.75 days of darkness. The Moon’s sidereal day is its actual rotation (and revolution) period of 27.32 days.

The motions of the Planets Each planet follows the same diurnal motion as the Sun, Moon and stars, rising in the east and setting in the west each day. Like the Sun and Moon, each planet moves eastward with respect to the stars. This is called direct motion. In addition, all the planets stay close to the ecliptic.

Two types of planets Superior planets – Mars, Jupiter, and Saturn Superior planets can appear on the meridian at midnight Inferior planets – Mercury and Venus Inferior planets always stay close to the Sun.

Discussion If we consider the Moon to be a planet, what type of planet would it be? Why?

Path of Mars

Merry-go-round

Ptolemy’s explanation for retrograde motion Each planet moves on a small circle called and epicycle. The center of each epicycle moves along a larger circle centered near the Earth called a deferent.

Ptolemaic system Very successful at predicting positions of the planets but was not perfect Offered no explanation of why the planets moved on deferents and epicycles There was no relationship between period of revolution and epicycle size

Alternatives to Ptolemy’s model Aristarchus proposed a heliocentric model of the Solar System in the 3rd century B.C.E. Reintroduced in the 16th century by Copernicus 1543

Heliocentric model Sun at the center Diurnal motion explained by rotation of the Earth All the planets including Earth revolve about the Sun in circular orbits with different speeds

Advantages of heliocentric model Provides natural explanation of retrograde motion. Provides natural explanation for the motion of mercury and Venus as inferior planets, i.e. their orbits are interior to that of the Earth. Provides a relationship between distance from Sun and orbital period. Planets farther from the Sun took longer to complete an orbit.

Retrograde motion

Inferior planets

Disadvantages of the heliocentric model Still required epicycles Was no better at predicting planetary positions No stellar parallax observed

Discussion How could you explain the the motion of the inferior planets Mercury and Venus with deferents and epicycles in the geocentric model?

Tyco Brahe

Tycho Brahe’s Epilepsy Medicine: The basic substance is the head of a person who has been hanged or otherwise executed. The head should be dried and crushed together with peony seeds to a powder. This medicine should not be taken at the full moon.

Tycho Brahe showed that the celestial sphere could change Tycho’s supernova of 1572 – showed that this new star had no parallax and thus was more distant than the Moon Comet of 1577 – showed that it too was beyond the distance of the Moon

Island Hven

Sextant

Mural Quadrant

Tycho Brahe Carefully tracked the position of the planets for 20 years to unprecedented accuracy in an attempt to disprove the ideas of Copernicus.

Galileo

Galileo Did not invent the telescope, but was the first to publish astronomical observations made with a telescope

Galileo’s Observations The Sun had spots which were considered imperfections The Moon had mountains and valleys The Milky Way resolved into countless stars Jupiter had four moons that clearly orbited it and not the Earth Venus had phases

Discussion Explain why the observations of the phases of Venus prove that Venus must orbit the Sun. Why is this different than the Moon, which also has phases but orbits the Earth?

Discussion Why did Galileo's observations of the orbits of the moons of Jupiter convince him that the Copernican model of the solar sydtem had to be correct?

Jupiter acted like a smaller version of the Solar System Jupiter is bigger than its four moons and the moons orbit it Jupiter’s moons orbit with periods that are longer for those moons that are furthest from the planet

Kepler’s first law of planetary motion The orbit of a planet about Sun is an ellipses with the Sun at one focus.

The semi-major axis is ½ the long axis of ellipse and equal to the distance of the planet from the Sun averaged over the entire orbit

Note that e needs to be significantly different than 0 for orbit to be noticeably different from a circle.

Kepler’s Second law of planetary motion A line drawn from the planet to the Sun sweeps out equal areas in equal intervals of time.

Kepler’s third law of planetary motion The square of the orbital period is equal to the cube of the semimajor axis (1/2 of the major axis) of the orbit.

Note The period of a planet in orbit about the Sun according to Kepler’s laws does not depend of the mass of the planet. The mass of an object orbiting the Sun, or the Earth, makes no difference to the object’s orbit.

Kepler’s laws Orbits of planets are ellipses, though nearly circular. Planets sweep out equal areas in equal times Square of orbital period is equal the cube of the semimajor axis P2 = a3

Galileo is arrested Galileo claimed that his observations proved the Earth must revolve about the Sun which was at odds with the teaching of the Church. In reality, his observations merely proved that Mercury and Venus orbited the Sun and not the Earth.

Galileo’s Physics The Earth’s gravity accelerates all objects, regardless of weight, by the same amount A moving object will stay in motion in a straight line at a constant speed unless acted upon by a force