When the Moon enters the Earth’s shadow it causes a LUNAR eclipse – at time of full moon only. Can see lunar eclipse from anywhere on earth.

Moon’s shadow falling on Earth causes SOLAR eclipse. There is a solar eclipse only in limited region of moon’s shadow. Solar eclipse occurs at full moon.

Solar eclipse

Lunar eclipse

AST101 Lecture 2 Jan. 27, 2002

Eclipses

Moon’s orbit is not exactly in the ecliptic plane. Can only get a solar eclipse when Earth, Sun and Moon line up exactly, so there is not an eclipse every month.

No eclipses if moon is above or below the Earth-Sun line.

Why is a solar eclipse more rare than a lunar eclipse?

Ecliptic (earth’s orbit plane)

One of the most basic things we need to know about an object in the universe is “How far away is it?”

So measurement of distances is a big deal in Astronomy, and there are a large range of methods used, with those used to get more distant objects based on those for nearer objects. Over the semester, we will discuss a set of methods used at ever larger distances (see next to last page of textbook). Typically the methods used for further objects are less precise.

For all objects in the universe except the sun and the planets in our solar system, we cannot visit and observe their nature at first hand. We have to infer the nature of stars, galaxies etc. just on the basis of the light and other radiation that they send us. The amazing thing is that despite this, we know so much!

The ‘cosmic distance ladder’ – sequence of methods to measure distances. We will build this ladder rung-by-rung.

Distances to astronomical objects

The solar system as we know it today

The planets orbiting the sun, going outward from Sun:o Mercury

o Venuso Eartho Marso (asteroid belt)o Jupitero Saturno Uranuso Neptune

o Pluto

(Uranus, Neptune, Pluto not known before telescopes)

The orbital planes of the planets are nearly the same (near the ecliptic), except for Pluto whose orbit is inclined at 17O

Planets rotate on axes in same sense as revolution around the sun. Our moon revolves around Earth in the same sense too.

Planetary sizes vary widely; Jupiter, Saturn, Uranus and Neptune are large and have many moons.

Radar distancing:

What is distance from Earth to Moon? (or to nearby planets)

Can measure by bouncing a radar pulse off the moon and measuring the time for the pulse to return. Call the time for pulse to return t (generally use to denote a difference or interval).

Earth Moon

d

Radar (Electromagnetic wave) travels at the speed of light.

Speed of light ( c ) = 186,000 mi/s = 300,000 km/s = 3 x 108 m/s = 3 x 1010 cm/s

Thus using distance = rate (speed) x time:

2 d = c t (2d since pulse goes to Moon and back again) or d = c t/2

Can measure t to nanosecond (10-9s) accuracy: Get d ≈ 385,000 km with error of a few meters (actually moon’s orbit around Earth is not circular, and d varies between 363,000 and 406,000 km over month)

radar pulse

What time interval is required for radar to go to moon and back?

How long does light travel going from sun to earth (1AU)?

Distance measurement by Parallax:

From plane geometry, we know that a triangle is completely fixed (3 sides and 3 angles known) if we know 2 angles and a side.

90o

s

Knowing angles 90O and measuring and s, one can obtain d without stepping on the crocodile.

Trigonometry: tan = s/d - or just make a scale drawing and determine d from it.

For astronomical objects, distance d is much larger than s (the ‘baseline’), and the angle in the diagram is a small angle.

sd

( Relation then simplifies: s = d (or d = s/) if is in radians )

is called the PARALLAX angle (s is the ‘baseline’). For fixed s, small means large d

d

To get distance to object in space, could measure the parallax angle using the diameter of the earth as baseline (observe the object relative to the very distant ‘fixed stars’ from a fixed location on earth 12 hours apart).

Exercise:

View your finger with outstretched arm, first with left eye and then with right eye. Apparent location of finger relative to the distant wall differs due to the parallax. The distance between your eyes is the baseline here.

bla

ckboard

To get to larger distance, can use a larger baseline – for example, use the baseline as the diameter of the earth’s orbit (2 AU). Measure the parallax angle for the Earth at opposite points on its orbit in January and July.

A nearby (red) star appears at different positions relative to the distant ‘fixed’ stars in Jan. and July.

Ancient’s view of the Universe

Sun, moon, planets and stars move on SPHERES in circular motion with constant angular speed – because the sphere is the ‘perfect’ figure, and the heavens are the work of a perfect creator.

The heavens are unchanging.

The ancient Greek astronomers made some basic assumptions about the Universe to guide their models:

The earth is at the center of the universe (geocentric universe) – we see the sun circling us daily; the moon changes its location in the sky over a month. The stars move in roughly a daily pattern.

The argument was made: Man is the most important creature in the universe, so the center of the universe is Man’s home. And if the earth were moving, we would feel it! (or fall off).

Venus

Moon

Sun

Fixed stars

The Greek’s basic idea: All bodies are attached to spheres centered on Earth. The sphere rotates around the earth in uniform motion carrying the heavenly body with it. The rates of the sphere’s motion differ: Sun and stars circle in about 1 day; Moon circles in ~1 month; Venus circles in over 1 year.

Earth

Simplified geocentric model with moving spheres carrying the Moon, Sun, fixed stars and known planets (Mercury, Venus, Mars, Jupiter and Saturn.

Motion of Sun and Moon, seen against the pattern of the stars, is west to east. For example if the Moon is in front of Orion one day, the next day, it will appear to east of Orion. Same with the Sun – over the course of the year, it moves through the constellations of the zodiac in an easterly direction.

(Mercury, Mars, Jupiter, Saturn not shown)

There are observational problems with a simple geocentric universe:

Even the Sun and moon appear to move non-uniformly with some deviation from circles. The planets deviate from uniform circular motion even more.

Planets – for example Mars – usually move against the stars in an easterly direction, but about once per year, reverse and move retrograde in westerly direction for a while before reverting to standard easterly motion.

Also Mercury and Venus are never found far from the Sun – with circular orbits around Earth, they should be found at any angle from Sun.

westeast

Ancient Greek’s made an ingenious hypothesis to ‘explain’ non-circular motion and retrograde motion while keeping the geocentric picture and circular motion: ‘epicycles’: A planet moves on a circle (called an epicycle), whose center moves in a circle around the earth (called the deferent). This system was brought to its final form by Ptolemy.

The center of the epicycle moves on the deferent. Varying the speed and size of the epicycle and deferent can give many different kinds of motion. (later slides)

earth

deferent

epicycle

planet

earth

Venus

To limit the maximum angle of Venus to the Sun, the velocity of Venus’ deferent should be exactly the same as Sun’s deferent.

Sun

Center of Venus epicycle, and Sun move at same angular speeds on their deferents. Maximum angle of Venus from Sun fixed by size of Venus epicycle (and radius of deferent).

To get all the motions of the sun, moon, major planets approximately right, Ptolemy required 80 separate circles, each with its own speed of rotation.

Note: will never see the full disk of Venus in light – always backlit by Sun

earth

If epicycle is fixed with no rotation to deferent, the dashed line motion of the planet is simply a larger circle. (The revolution on the deferent rotates the epicycle with it.)

earth

If epicycle rotates twice as rapidly as the deferent, the dashed line motion of the planet is an oval. (In this figure, when ¼ turn is made on deferent, the planet moves ½ turn on the epicycle, so planet at A is all the way outside the deferent and at B is all the way inside.)

A

B

Plot the shape of a planet’s orbit if it moves on the epicycle in the opposite sense as the motion on the deferent but with the same angular speed.

Examples of epicycle motion:

earth

If epicycle rotates three times as rapidly as the deferent, the dashed line motion of the planet shows retrograde motion. (The backward motion while the planet is inside the deferent is greater than the forward motion due to revolution of epicycle on the deferent.)

By varying the size of epicycle and deferent, and speed of revolution on epicycle and deferent, Ptolemy was able to give an approximate representation of the planetary motion.

But the accuracy was not good! (failed to predict dates of eclipses etc.)

The system was very cumbersome with all those 80 arbitrary numbers needed to describe it.

The price to pay for retaining circular motion centered on Earth was large. Does this look ugly or what?