Kepler's Laws and Early Astronomy Discoveries

Ellipse

An elongated circle.

Foci

End of ellipse; they are points located inside the ellipse.

Location of foci

If the ellipse is nearly a circle, the foci are closer to the centre; if the ellipse is very stretched out, the foci are farther from the centre.

Eccentricity

A number that measures how much the ellipse shifts from being a perfect circle.

Eccentricity range

The eccentricity of an ellipse is always between 0 and 1.

E = 0

Perfect ellipse (circular).

E close to 1

More elongated or stretched.

Major axis

Longest diameter of the ellipse passing both foci.

Minor axis

Shortest diameter of the ellipse perpendicular to the major axis at its centre.

Semi major

Half of the major axis.

1st law

Planets don't move in perfect circles; their paths are slightly stretched-out circles (ellipses), and the Sun is off-center at one special point inside the ellipse.

2nd law

Planets move faster when they are closer to the Sun and slower when they are farther from the Sun; the area covered by the planet in its orbit in a fixed time is always the same.

Perihelion

When the Earth is closest to the Sun in its orbit, it moves fastest there.

Aphelion

When the Earth is the furthest away from the Sun in its orbit, it moves slowest there.

3rd law

The square of the orbital period of a planet increases as the cube of the semi-major axis of its orbit increases.

P

Period of revolution (orbital period in Earth years).

a

Semi-major axis (average distance from the Sun in AU).

1 AU

Earth's distance from the Sun.

Kepler's contribution

Kepler talked about the orbital period in terms of orbits per time, describing how many times a planet goes around the Sun in a certain amount of time.

Rudolphine tables

Published in 1627, they were the most accurate astronomical tables of their time, predicting the positions of planets and stars.

Significance of Rudolphine tables

They proved heliocentrism and laid groundwork for Kepler's laws, inspiring Newton's theory of gravity.

Galileo Galilei

Remembered as the father of the scientific method.

Galileo's observation of the Moon

He noted smooth, dark patches (cooled lava) and mountains, measuring heights (~7 km) using trigonometry.

Galileo's observation of the Milky Way

He proved it was countless stars, contradicting Aristotle's claim that it was an atmospheric phenomenon.

Planets vs. Stars

Planets appeared 100x larger through telescopes; stars remained point-like due to distance.

Galilean Moons of Jupiter

Names: Io, Europa, Ganymede, Callisto (originally called 'Medician stars').

Significance

First direct evidence not everything orbits Earth (contradicted Aristotle).

Ganymede

Largest moon in the solar system.

Phases of Venus

Venus shows crescent, gibbous, and full phases (like the Moon).

Proof of Heliocentrism

Phases only make sense if Venus orbits the Sun (not Earth).

Ptolemaic Model Failed

Could not explain Venus's full phase.

Sunspots

Dark, cooler regions (~1000°C cooler than the Sun's surface).

Significance of Sunspots

More evidence against 'perfect heavens.'

Starry Messenger (Sidereus Nuncius, 1610)

Published observations.

Dialogue Concerning the Two Chief World Systems (1632)

Mocked geocentrism (Pope's arguments voiced by 'Simplicio').

Inquisition (1633)

Forced to recant heliocentrism; sentenced to house arrest.

Galilean Refractor

Design: Convex primary lens + concave eyepiece.

How Galilean Refractor Works

Light refracts through glass lenses; primary lens concentrates light, eyepiece refocuses rays for the eye.

Limitation of Galilean Refractor

Narrow field of view.

Keplerian Refractor (Modern)

Design: Two convex lenses (inverted image).

Advantages of Keplerian Refractor

Wider field of view, brighter images.

Disadvantage of Keplerian Refractor

Image appears upside down; does not correct aberration.

Plenism

No vacuum; universe filled with 'aether.'

Three Corpuscles

1. Luminous: Tiny particles → stars. 2. Opaque: Planets (e.g., Earth). 3. Transparent: Space filler ('aether').

Vortex Motion

Stars spin, creating whirlpools that carry planets.

Micrographia (1665)

First use of the word 'cell' (biology).

Air Pumps

Proved vacuums exist (with Boyle).

Gravity Framework (1674)

1. All celestial bodies attract toward their centers. 2. Gravity weakens with distance (inverse-square law idea). 3. Objects move straight unless deflected (pre-Newton inertia).

Isaac Newton's Breakthroughs

1. Calculus: Invented to solve physics problems (e.g., planetary motion). 2. Optics: Dispersion: White light → ROYGBIV (red bends least, violet most). 3. Laws of Motion & Universal Gravitation: Force ∝ masses; inversely ∝ distance².

Tides

Caused by Moon's gravity (stronger on near side → bulges).

Spring Tides

Sun + Moon align (new/full Moon → extreme tides).

Neap Tides

Sun/Moon at 90° (quarter phases → weak tides).

Great Comet of 1680

Newton proved comets obey Kepler's laws.

Halley's Comet

Predicted 1758 return (76-year period).

Discovery of Uranus (1781)

First planet discovered by telescope (March 13, 1781).

Moons of Uranus

Titania & Oberon (brightest moons, named after Shakespeare/Pope characters); later found: 27 moons total.

Uranus' Unique Features

Axial Tilt: 98° ('on its side'); 21-year polar day/night cycles.

Axial Tilt

98° ('on its side'); 21-year polar day/night cycles.

Rings of Uranus

Discovered in 1977 (Voyager 2 confirmed).

Density of Uranus

Higher than Jupiter/Saturn → ice giant (methane atmosphere → blue color).

Herschel's Telescopes

Built largest telescope (40-foot, 1789; flawed but revolutionary).

Binary stars

Discovered by Herschel (e.g., Polaris is triple).

Martian polar caps

Discovered by Herschel.

Nebulae

Herschel discovered 2,500+ nebulae (later identified as galaxies/star clusters).

Stellar Parallax Assumption

Incorrectly assumed all stars have equal brightness → brighter stars = closer.

Caroline Herschel

First paid female astronomer (£50/year by King George III).

Comets Discovered by Caroline Herschel

Discovered 8 comets (e.g., 35P/Herschel-Rigollet, 155-year orbit).

Catalogue of Nebulae

Co-authored by Caroline Herschel (2,500 entries).

Globular Clusters

Spherical star groups (e.g., Hercules Cluster).

Titius-Bode Law

Predicts planet distances.

Successes of Titius-Bode Law

Predicted Uranus (n=6: 19.6 AU vs. actual 19.2 AU).

Search for Missing Planet

Led to search for missing planet at n=3 (2.8 AU).

Failure of Titius-Bode Law

Neptune deviated (30 AU vs. predicted 38.8 AU).

Ceres

First asteroid discovered (1801, Piazzi); dwarf planet (940 km wide).

Asteroid Belt Mass

Total mass: ~4% of Moon's mass.

Neptune's Discovery

Cause: Uranus' orbit anomalies → predicted by Le Verrier & Adams using Newtonian gravity.

Galle's Discovery of Neptune

Found it at Berlin Observatory (within 1° of prediction).

Moons of Neptune

Triton (largest, retrograde orbit, -235°C).

Nebular Hypothesis

Solar System Formation: Collapse of rotating gas/dust cloud → flattened disk → planets form.

Frost Line

Boundary where volatiles (e.g., H₂O) freeze (~3 AU).

Martian Opposition

When Mars and Earth are closest (best time to observe Mars).

Martian Conjunction

When Mars and Earth are farthest apart.

Discovery of Martian Moons

Asaph Hall found Phobos and Deimos (Mars' two moons) using a 26-inch telescope.

Phobos

Closer to Mars; orbits faster than Mars rotates (completes an orbit in 7.7 hours).

Deimos

Farther, takes 30 hours to orbit.

Martian Canals

Giovanni Schiaparelli (1877) saw lines on Mars and called them 'canali' (Italian for channels).

Truth Revealed about Martian Canals

NASA's Mariner 4 flew by Mars and saw no canals—just craters!

Discovery of Pluto

Found by Clyde Tombaugh at Lowell Observatory in 1930.

Blink Comparator

Machine that compares photos to spot moving objects.

Charon

Biggest moon of Pluto, discovered in 1978.

Kuiper Belt

Location: Beyond Neptune (30-50 AU from the Sun).

Icy leftovers

Leftovers from the solar system's formation, like Pluto.

Short-period comets

Comets that take less than 200 years to orbit the Sun.

Oort Cloud

Location: Super far away (2,000-200,000 AU).

Long-period comets

Icy chunks that become comets, like Halley's Comet.

Astronomical Unit (AU)

Earth-Sun distance (~150 million km). Good for solar system.

Light-Year (ly)

Distance light travels in 1 year (~9.5 trillion km or 63,000 AU).

Proxima Centauri

4.2 light-years away, light takes 4.2 years to reach us.

Parsec (pc)

Distance where a star has 1 arcsecond parallax (3.26 ly).

Parallax Method

Measure a star's apparent shift when observed 6 months apart (baseline = 2 AU).