# Astronomy Notes

## Part 2: Solar System Layout

John P. Pratt

### Early Greek Astronomy

The Greeks deduced several basic astronomical results.

• The lunar phases imply the moon is spherical, rather than a flat disk.
• Lunar phases imply that the moon is between the earth and the sun.
• Lunar eclipses imply that the earth is spherical because it has a round shadow.
• The earth is spherical because as one goes north, southern stars disappear below the horizon.

Aristotle's scientific evidence that the earth is the center of the universe (300 B.C.).

• Parallax means that nearby objects seem to move relative to distant objects when viewed from different places.
• If the earth were moving, then nearby stars should move relative to distant stars.
• Careful observations of many stars showed that none of them had any measurable parallax shift.
• Hence, it was concluded that the earth is the center of the universe, which dominated thought for 1,800 years.
• The reason for the failure was that the stars are so distant, the parallax of even the nearest star is less that 1".

Eratosthenes and the Size of the Earth (200 B.C.)

• He read that the sun casts no shadow down a well at Syene at the summer solstice.
• He measured that shadows in Alexandria on that day were about 1/50th of a circle.
• He deduced that the circumference of the earth must be 50 times the distance between those cities.

Hipparchus and Precession (100 B.C)

• He observed stars and compiled a star map of some 850 stars.
• He noticed that the positions relative to the equinoxes had moved.
• The shift of 1° every 72 years is called the precession of the equinoxes.
• It is caused because the earth's axis of rotation draws a circle in the sky every 26,000 years.

Ptolemy's Epicycles (A.D. 150)

• Retrograde Motion. The outer planets make loops every year across the zodiac constellations as the earth passes them.
• Ptolemy explained that motion with epicycles: planets circling empty centers, which in turn circled the earth.
• Alexandria fell to the Arabs in A.D. 640.
• His book became the Bible of astronomy for some 1400 years at the downfall of Greek thought.

### Renaissance Discoveries

Copernicus proposes a sun-centered system

• Occam's razor is the principle that the simplest theory that explains the facts is the best.
• A sun-centered solar system is much simpler than an earth-centered; that was the principal argument favoring it.
• He answered Aristotle's argument by correctly proposing that the stars are extremely far away.

Tycho made careful planetary observations in 1500's using a huge quadrant (before the telescope).

Kepler uses Tycho's observations to proposed Kepler's Laws:

1. Each planet moves in an ellipse with the sun at one focus.
2. The line connecting the sun and the planet sweeps out equal areas in equal times.
3. P2 = a3. The squares of the planetary periods in years equals the cubes of the semi-major axes in a.u. (1 a.u. = astronomical unit = distance from earth to sun).

Galileo began using the telescope in 1610 to make many key astronomical discoveries

• Jupiter has moons orbiting it, so the earth is not the center of all celestial motion.
• The sun has spots and the moon has mountains, so they are not polished spheres.
• Venus has a gibbous phase, which disproved Ptolemy's epicycles, which predicted only crescent phases.

Newton, the greatest physicist of all time, discovered Newton's Three Laws of Motion

1. A body stays at rest or in motion in a straight line at the same speed unless acted on by a force.
2. If a body accelerates, it is being pushed by a force such that Force = mass x acceleration (F = ma).
3. For every force on one body, there is an equal and opposite force reacting on another body.

Newton's Law of Gravity

• The gravitational force between two bodies is proportional to their masses, and inversely as the square of the distance separating their centers.
• In other words, F = GMm/r2, where G is called the gravitational constant.
• The bigger M is the more you weigh. If the earth were all made of rock, so that it were only 1/2 as massive, then we would all weigh half as much.
• If r doubles, then the force of gravity drops to 1/4.
• Both can vary at once: The moon is 1/80 as massive and 1/4 the radius of the earth, so one would weigh (1/80)/(1/4)2 = 16/80 = 1/5 as much.

Why all things fall at the same rate (ignoring air resistance)

1. F = ma from Newton's second law of motion.
2. F = GMm/r2 is Newton's law of gravity.
3. ma = GMm/r2 because both are equal to the force F.
4. a = GM/r2 after dividing both sides my the mass m.
5. That means that the acceleration is the same for any mass m.

Bode's Rule

• About 1770 Bode taught that the planets are spaced according to a simple rule, except one planet was missing between Mars and Jupiter.
• About 1780 a new planet, Uranus, was discovered at the spacing predicted by Bode's rule.
• About 1800 the first asteroid was discovered at the position of the missing planet.
• Planetary moons, like those around Jupiter and Saturn also follow a form of Bode's rule.
• Bode's rule is still not well understood, although it has been simulated by computers.