Birth of Modern Astronomy

Learning Objectives

• Explain Brahe and Kepler's relationship to the discovery of planetary motion.
• Understand the importance of the laws of planetary motion.
• Elaborate on the contributions of notable modern astronomers.
• Assess the relations between ancient and modern astronomy.

The Birth of Modern Astronomy

• Five scientists made discoveries that led to modern astronomy, 14 centuries after Ptolemy.

Isaac Newton

• He developed and formalized Galileo's concept of inertia.
• He conceptualized the force of gravity.
• He provided an explanation for elliptical orbits.

Nicolaus Copernicus

• He was a student of Plato.
• He believed the Earth is spherical because it casts a curved shadow during lunar eclipses.
• Copernicus proposed the heliocentric, or sun-centered, system.
• He theorized that the Sun is at rest near the center of the Universe.
• The Earth spins on its axis daily and revolves annually around the Sun.

Tyco Brahe

• Brahe thought that only the Sun and Moon revolved around the Earth.
• Other planets revolved around the Sun, which itself revolved around the Earth.
• He was a Danish astronomer and nobleman.
• Made accurate observations of celestial bodies.
• King Frederick II of Denmark sponsored him in 1576.
• Brahe invented astronomical instruments and made extensive studies of the solar system with the help of his assistants.

Johannes Kepler

• Used Brahe's data to formulate the three laws of planetary motion.
• The three laws of planetary motion are the law of Ellipses, the law of Equal Areas, and the law of Harmonies.
• He was born to a poor German family.
• Kepler studied as a scholar at the University of Tubingen in 1589.
• Emperor Rudolf II recommended Johannes Kepler to work for him as as assistant
• When Kind Frederick II died, the successor did not support Brahe's work.

Galileo Galilei

• Greatest Italian scientist of the Renaissance.
• His use of the telescope allowed for observing astronomical details.
• Galileo observed the Moon, phases of Venus, moons around Jupiter, and sunspots.
• He discovered that countless individual stars make up the Milky Way Galaxy.
• Galileo's observations sparked the birth of modern astronomy.

Kepler's Laws of Planetary Motion

• Kepler's Laws are the law of Ellipses, law of Equal Areas, and law of Harmonies.

Astronomical Terms

• Astronomical Unit (AU): Defined as the average distance between Earth and the Sun, which is about 1.5 x 10^8 kilometers or 1.5 x 10^11 meters.
• Eccentricity: In an ellipse, it's the ratio of the distance between the foci to the major axis.
• Ellipse: A closed curve where the sum of distances from any point on the ellipse to two points inside (foci) is constant.
• Focus: One of the two fixed points inside an ellipse from which the sum of the distances to any point on the ellipse is constant.
• Major Axis: The maximum diameter of an ellipse.
• Orbit: The path of an object in revolution around another object or point.
• Orbital Period: The time it takes an object to travel once around the Sun.
• Orbital Speed: The speed at which an object (usually a planet) orbits around the mass of another object.
• Semimajor Axis: Half of the major axis of a conic section, such as an ellipse.

Kepler's First Law

• Each planet moves around the Sun in an orbit that is an ellipse.
• The Sun is located at one focus of the ellipse.

Kepler's Second Law

• The straight line joining a planet and the Sun sweeps out equal areas in space during equal intervals of time.

Kepler's Third Law

• The square of a planet's orbital period is directly proportional to the cube of the semimajor axis.

Law of Ellipses

• Planets follow an oval or ellipse orbit, instead of a circular path.
• This orbit matched calculations and explained the "irregularities" in the movement of Mars.
• The law describes the actual elliptical path followed by planets with the Sun at one focus.

Law of Equal Areas

• An imaginary line drawn from the center of the Sun to the center of a planet sweeps out equal areas of space in equal time intervals.
• Describes how fast a planet moves in orbit, moving fastest when closest to the Sun and slowest when farthest, with the line sweeping equal areas in equal time.

Law of Harmonies

• The ratio of the squares of the periods of two planets is equal to the ratio of the cubes of their average distances from the Sun.

Isaac Newton

• Established the Law of Universal Gravitation
• Agreed that the Earth rotates around the Sun.
• Newton's three laws of motion and law of gravitation provided a foundation for understanding planetary motion.
• Provided rationale that explained Kepler's three laws.

Brahe and Kepler's Collaboration

• Brahe mistrusted Kepler and hesitated to share astronomical data, fearing his assistant would overshadow him.
• Brahe assigned Kepler to interpret observations of Mars, whose movement didn't align with Brahe's calculations.
• Kepler was tasked to figure out what path Mars followed as it revolved around the Sun.
• Some believe Brahe gave Kepler the task to keep him occupied so Brahe could develop his laws of planetary motion.

Kepler's Discoveries

• Kepler postulated a force from the Sun moves the planets.
• Kepler concluded this force explained the orbit of Mars and the Earth, including all other planets.
• The planets moved the fastest when nearest the Sun and slowest when farthest from the Sun.
• The Rudolphine Tables, named after the Roman emperor, are useful for determining the positions of the planets.