Comprehensive Astronomy: Planets, Kepler, Newton, and Galileo

Planet

derived from a Greek term meaning wanderer.

Known Planets

The planets that were known before the telescope was invented were Saturn, Venus, Mars, Mercury, and Jupiter.

Direct Motion

When observing planetary motions from the Earth, the phrase refers to the slow eastward motion of the planet from night to night compared to the background stars.

Retrograde Motion

An apparent westward motion of a planet from night to night compared to the background stars (as viewed from the Earth) is referred to

Celestial Sphere Motion

When viewed from the Earth, the celestial sphere (the background of stars) moves east to west on a daily basis. This motion is caused by the rotation of the Earth on its axis.

Copernican System

Nicolaus Copernicus was the first person to develop a comprehensive model for a Sun-centered solar system.

Sidereal Period

a planet is defined as the time between two successive passages of the planet in front of a particular point in the sky (e.g., a star) as seen from the Sun.

Synodic Period

The time period between two successive passages of a planet through the position of opposition is

Planetary Orbits

A significant contribution of Kepler to our understanding of the solar system was the discovery that planetary orbits are not circular.

Kepler's First Law

Kepler's first law states that a planet moves around the Sun in a(n) elliptical orbit, with the Sun at one focus.

Eccentricity

The eccentricity of a planet's orbit describes its shape compared to that of a circle.

Major Axis

The distance from the perihelion point to the aphelion point of a planetary orbit is the major axis.

Semimajor Axis

The semimajor axis of an ellipse is the distance from the center of the ellipse to one end, along the largest diameter of the ellipse.

Perihelion

To which point in a planetary orbit does the word perihelion refer? point closest to the Sun.

Aphelion

point farthest from the Sun.

Planet's Speed at Aphelion

At what point in a planetary orbit is the planet's speed the slowest?

Kepler's Second Law

Kepler's second law states that a planet moves fastest when it is closest to the Sun.

Kepler's Third Law

Kepler's third law, the harmonic law, provides a relationship between a planet's orbital period and the length of the semimajor axis.

Orbital Period and Semimajor Axis Relationship

Kepler's third law tells us that the square of a planet's period in years is the same number as the cube of its semimajor axis in AU.

Simplified Kepler's Third Law

In the simplified version of Kepler's third law, P2 = a3, the units of the orbital period P and the semimajor axis of the ellipse a must be, respectively, years and astronomical units.

Halley's Comet

Halley's Comet returns to the Sun's vicinity approximately every 76 years in an elliptical orbit.

Halley's Comet

Halley's Comet returns to the Sun's vicinity approximately every 76 years in an elliptical orbit.

Semimajor axis of Halley's Comet

According to Kepler's third law, the semimajor axis of this orbit is 17.9 AU.

Comet with a period of 31.7 years

A comet is observed to return to the vicinity of the Sun on a long elliptical orbit with a period of 31.7 years; the semimajor axis of the orbit is 10 AU.

Galileo's observations of moons

Galileo's observations of moons orbiting Jupiter disagreed with the theory of the universe accepted up to that time because the moons did not orbit the Earth.

Geocentric model belief

The fundamental belief about the universe, established by the Greeks and adopted by the early Christian church, was that everything in the universe orbits the Earth.

Phases of Venus

Galileo's early observations of the sky with his newly made telescope included the discovery of the phases of Venus.

What Galileo did not observe

Galileo did NOT observe Uranus with his new telescope.

Visible phase of Venus in geocentric model

In the geocentric model of the solar system, the new phase of Venus should be visible from Earth.

Significance of Jupiter's moons

Galileo found it significant that the moons farther from Jupiter had longer periods, just as Copernicus had discovered for the planets around the Sun.

Jupiter's size based on moons

The observation that Jupiter has satellites (moons) showed that Jupiter must be four times the size of the Earth (because Jupiter has four moons and the Earth has one).

Newton vs. Kepler

The most important difference between the development of Isaac Newton's theory of planetary motion and that of Johannes Kepler is that Newton developed his theory from basic physical assumptions, whereas Kepler simply adjusted his theory to fit the data.

Newton's contribution to astronomy

Newton showed that astronomical phenomena can be explained using only basic physics and mathematics.

Importance of Newton's laws

Newton's laws showed that planets can move around the Sun by themselves forever, without coming to rest.

Newton's first law

According to Newton's first law, if no net force is acting on an object, then both the object's speed and direction of travel will be constant.

Earth's movement without Sun's gravity

If the Sun's gravitational force were suddenly removed from it, the Earth would move in a straight line along a tangent to its circular orbit.

Constant velocity and acceleration

A body whose velocity is constant has zero acceleration.

Acceleration definition

The acceleration of a moving body is defined as the rate of change of velocity with time.

Newton's second law

Newton's second law states that force equals mass times acceleration.

Constant force and acceleration

According to Newton's second law of motion, an object acted on by a constant force always moves with a constant acceleration.

Newtonian mechanics of solar system

The Newtonian understanding of the mechanics of the solar system states that the natural motion of the planets is motion in a straight line, prevented by the gravitational force of the Sun.

Why Earth doesn't fall into the Sun

The Sun exerts a gravitational pull on Earth; Earth is moving across the Earth-Sun direction, so it is pulled around in a circle.

Object orbiting the Sun

An object orbiting the Sun in a circle can be said to be always accelerating.

Newton's third law

According to Newton's third law, if a force is acting on an object, then there must be some other force acting on a different object, with the same magnitude but in the opposite direction.

Action-reaction pair example

An example of an action-reaction pair by Newton's third law is for a dog pulling on its leash, the force of the dog on the leash and the force of the leash on the dog.

Diver's force during back flip

A diver weighing 138 pounds exerts a force of 138 pounds on the Earth while doing a back flip.

Asteroids and gravitational force

If two asteroids are located at the same distance from the Sun, and one asteroid has twice the mass of the other, the more massive asteroid feels twice the force that the other does according to Newton's law of gravitation.

Law of gravitation formula

The law of gravitation expounded by Newton for the force F between two objects of masses M and m with separation (between centers) of R is given by F = GMm/R².