2.2 Brahe and KeplerData Gathering

- Tycho Brahe (1580) makes observations of planetary motion with improved accuracy.

- J. Kepler (1609) finds that these are consistent with the Heliocentric model governed by three laws.

Kepler’s Laws

1. Orbit of a planet is an ellipse with the Sun at one focus.

- An Ellipse is a squashed circle with two foci, such as the sum of the distances of any point to the foci

is the same (http://astro.unl.edu/classaction/animations/renaissance/kepler.html).

- An ellipse is characterized by its Semiminor Axis which is half of the line perpendicular to the line

between the foci. The Semimajor Axis is half of the line that divides the ellipse and passes between

the foci.

- An ellipse can be characterized by one of them (typically the Semimajor Axis) and the Eccentricity.

- "The orbital eccentricity of an astronomical object is a parameter that determines the amount by

which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit,

values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a

hyperbola."

- What’s at other focus? Nothing, not even the same for all planets.

- Eccentricity small: 0.017 for Earth, 0.2 for Mercury

2. Law of equal areas: The line from the Sun to planet sweeps out equal areas in equal times.

- Planet moves faster near perihelion (point closest to the Sun), slower near aphelion (point further

from the Sun).

- Comets in highly eccentric orbits – dramatic effect.

- This tells us the relative speed.

3. Square of sidereal period proportional to the cube of the Semimajor Axis

Astronomical Unit:

2=4∗2∗ Galileo’s Smoking Scope

- New technology: Galileo (1610) turns telescope up.

- Finds

o Phases of Venus showing it orbits the Sun: A New Venus happens when it is near the Earth, and a

Full Venus happens when it is at the other side of the Sun from Earth (fits the Keplerian model).

o Galilean moons orbiting Jupiter: it has satellites.

o Mountains on Moon, spots on Sun, ears on Saturn

- Also studied Mechanics (science of motion) and formulated the Principle of Inertia: An object will

retain its state of motion unless disturbed externally.

- To really get Mechanics, Newton had to invent Calculus.

This is Progress

- Galileo studies heavens as a physical system to be observed

- Kepler’s Laws predict planetary motion with unprecedented accuracy from simple model

- They are universal. In fact, they govern orbiting systems from Solar System to Saturn’s moons to… 

electrons in an Atom (with different K)

- Such universality is a hint of underlying fundamental laws

- It took Newton and new math to find them