Astronomy: History - Renaissance

200 B.C. -1400 AD:

In Europe, nothing....

Chinese observed supernova in 1054 as "guest star" in Taurus.
Brighter than Sirius, probably brighter than Venus. No European Records!

Il sole no si muove (The sun does not move) Leonardo da Vinci

COPERNIKUS (1473-1543)

Ptolemy's model by now required 40 epicycles to explain the increasingly accurate observations. Copernicus proposed a Heliocentric solar system model as a device to explain the motions. His model used circular orbits (thus still needing epicycles to achieve good agreement with observations).

Motion of Mercury & Venus "unlocked" from sun.

Lack of parallax because fixed stars are very far away

So why did people at the time believe in Copernicus? Reasons for asserting the earth is motionless:

1. David in Psalm 89: God has founded the earth and it shall not be moved.
2. Joshua bade the sun stand still-which would not be notable were it already at rest.
3. The earth is the heaviest element, therefore it more probably needs rest.
4. Everything loose on the earth seeks its rest on the earth, why should not the whole earth itself be at rest?
5. We always see half of the heavens and the fixed stars also in a great half circle, which we could not see if the earth moved, and especially if it declined to the north and south...
6. A stone or an arrow shot straight up falls straight down. But if the earth turned under it, from west to east, it must fall west of its starting point.
7. In such revolutions houses and towers would fall in heaps.
8. High and low tide could not exist; the flying of birds and the swimming of fish would be hindered and all would be in a state of dizziness.

Reasons for the belief that the earth is moved:

1. The sun, the most excellent, the greatest and the midmost star, rightly stands still like a king while all the other stars with the earth swing round it.
2. That you believe that the heavens revolve is due to ocular deception similar to that of a man on a ship leaving shore.
3. That Joshua bade the sun stand still Moses wrote for the people in accordance with the popular misconception.
4. As the planets are each a special created thing in the heavens, so the earth is a similar creation and similarly revolves.
5. The sun fitly rests at the centre as the heart does in the middle of the human body.
6. Since the earth has is itself its especial centrum, a stone or an arrow falls freely out of the air again to its own centrum as do all earthly things.
7. The earth can move five miles in a second more readily than the sun can go forty miles in the same time.

Voight (1667). Der Kurstgunstein Einfalt Mathematisher Raritaten Erstes Hundert.

Tycho Brahe 1546-1601 Note the tin nose ...
Ruler of island of Hveen (of coast of Denmark). Constructed Uraniborg (first observatory) to measure position of planets and stars

Now it is quite clear to me that there are no solid sphere's in the heavens, and those devised by the authors to save the appearances exist only in the imaginations for the purpose of permitting the mind to conceive the motion which the heavenly bodies trace in their courses. Brahe

KEPLER:

Corresponded with Brahe and acquired records after his death.

1) Planets move in ellipses, with the Sun at one focus.

An ellipse is the path drawn by a point which moves such that the sum of its distance from two fixed points is kept constant. Relations for ellipses: a is the semi-major axis b is the semi-minor axis r1 + r2 = 2a (why?)

The eccentricity, e, measures the deviation from a circle.

b = a(1-e²)1/2

The equation of the directrix is: r₁ = a(1-e²)/(1+e cosφ)

2) A vector drawn from the planet to the sun will sweep out equal areas in equal times. This means that "The planet moves faster when closer to the sun"

3) The period (P) and the semi-major axis (a) are related according to the expression

P²/a³ = a constant

eg

Planet	Period	Radius
Mercury	88 days	57.9x106 km
Venus	245 days	108.2x106 km
Earth	365 days	149.6x106 km
Mars	687 days	227.9x106 km
Jupiter	4333 days	778.4x106 km

These numbers are taken out of KKOPD. Find which one is wrong!

Note that Kepler's Laws are empirical laws: there is no indication yet of why they hold true...

GALILEO (1564-1642)

1. Developed telescope

2. Sunspots showed sun "imperfect" (and allowed him to measure rotation rate)

3. Phases of Venus.Probably most important, since it showed planets shone by reflected light: phases did not agree with Ptolemy

4. Moons of Jupiter. This is his original notebook: showed conclusively that objects other than earth could act as centre of orbit
   and this is a translation.

   The moons were simultaneously discovered by a German astronomer Marius (or Mayr). These moons are usually known as the Galilean Moons, although Marius gave them their names Io, Europa, Ganymede and Callisto. The probe to Jupiter which arrived Dec 7th 1995 was known as "Galileo".

5. Mountains of Moon. Showed heavenly bodies "Imperfect": can see shadows changing on edge of crates

6. Rings of Saturn: He also saw these, but he could never figure out what they were! He thought that the planet had "handles".

7. The greatest discovery Galileo never made!

   For a week in 1612, Neptune was in the field of his telescope when he was observing Jupiter, and he even notes that it seemed to be a moving star

Born the day of Galileo's death.

Newton's Discovery of the law of universal gravitation.

Why does the moon take 27.3 days to orbit the earth? Obviously: v = 2πR/P, where P is the period. Centripetal force: F = m v²/R Gravitation: F = mg So how does the moon stay up? BY FALLING!

A hypothetical ball thrown horizontally from a hypothetical tall tower, erected on the earth, will strike the ground a distance away from the base of the tower. A stable orbit is achieved when the ball travels with an initial tangential velocity which achieves a balance between the acceleration (falling) due to gravitational attraction, and the additional altitude achieved due to the curvature of the earth below the ball. That is, it falls due to the force of gravity (F=mg), but still maintains its altitude due to the centripetal force (F = m v²/R)

From:

v = 2πR/P
F = m v²/R

F = 4π²mR²/RP²

3) P²/a³ = a constant = k

What kind of gravitational force can give this relationship?

Then combining 1), 2), and 3), we get

F = 4π²m/ka²

The Law Of Universal Gravitation: F = GM_sunM_planet/R²

It applies between any two bodies anywhere in the universe.

Applying it to the earth-moon system: We need to know the mass of the earth (M_earth) and G. (We won't need the mass of the moon, since it will eventually cancel out.) F = GM_earthM/R²

We do know g at the earth's surface. The graviational force on objects near the earth's surface is F = mg. ...and these equations must agree.

Mg = GMearthM/R²earth
F = gMmoonR²earth/R²moon orbit

P = 2π(R³moon orbit/gR²earth) = 27.4 days

This is the first time that laws deduced on the Earth were seen to apply elsewhere!

The extra ingredients (measured later) are the individual values of M and G. Now we know G = 6.67x10^-11N kg^-2 m² and M_earth = 6x10²⁴ kg (Actually, Newton could have guessed M_earth: How?)

Note that we have assumed circular orbits for the time being. We will prove Kepler's 1st, 2nd and 3rd laws later on.

From now on, a purely 20th century perspective on Astronomy...We'll start in 1960