Tycho Brahe, Kepler, and the Nature of Science

Tycho Brahe

• Built instruments to measure the positions of planets very accurately (approximately 1 arc minute).

• Discovered that comets move outside of the Earth’s atmosphere.

• Observed a supernova and concluded it was much farther away than any celestial sphere.

• Held that the planets go around the Sun, but the Sun, in turn, orbits around the Earth because he could not detect parallax motion in the stars.

Kepler

• Developed empirical rules to describe the orbits of planets.

• Empirical science describes how something works, not why.

Kepler's Laws of Planetary Motion

• 1st Law: Planets move in elliptical orbits with the Sun at one focus.

• 2nd Law: Orbits sweep out equal areas in equal times.

• 3rd Law: More distant planets orbit at slower average speeds, described by the equation: $p^2 \propto a^3$ where $p$ is the period of the orbit and $a$ is the average distance of the planet from the Sun.

Eccentricity of Ellipses

• Eccentricity is defined as $e = \frac{c}{a}$, where $c$ is the distance from the center of the ellipse to one focus, and $a$ is the semi-major axis (the distance from the center to the furthest point on the ellipse).

Eccentricities of Planetary Orbits

• Orbits of planets are virtually indistinguishable from circles.

  • Earth: $e = 0.0167$

  • Pluto: $e = 0.248$ (most extreme example)

Kepler's 2nd Law: Equal Areas in Equal Times

• A line connecting the Sun to the planet sweeps out the same area in a given time, regardless of the planet's position in its orbit.

• Consequently, a planet moves faster when it is closer to the Sun.

Kepler's 3rd Law

• Deals with the relationship between a planet's average distance from the Sun and its orbital period.

• A planet closer to the Sun has a shorter orbital period.

• The period doesn't depend on the mass of the planet, only its distance from the sun.

• Expressed as: Period$^2$ is proportional to Distance$^3$.

• $p^2 \propto a^3$

Third Law Consequences

• Distant planets take longer to orbit the Sun.

• Distant planets travel at slower speeds.

The Nature of Science

• Science is a method for understanding the world, not just a collection of facts.

• The scientific method relies on evidence from nature (observations and experiments) and does not consider non-natural sources of knowledge.

• The key feature of scientific theories is their ability to explain and predict observable phenomena.

Science vs. Non-Science

• Distinguishing factors of science:

  • Only natural causes are considered.

  • Models are created and tested to explain observations as simply as possible.

  • Testable predictions are made.

  • Models are revised or abandoned if they do not conform to observations.

• Non-science (or pseudo-science) does not adhere to these rules (e.g., ESP, Astrology).