Astronomy - Chapter 2

Kepler's second law implies what about planetary motion?

A planet moves faster when it is closer to the Sun.

What would happen to the orbits of each of the planets if the force of gravity was suddenly "turned off"?

Each would move off in a different straight line.

the acceleration of an object is directly proportional to the applied force and inversely proportional to its mass - when a force F acts on a body of mass m, it produces in it an acceleration a equal to the force divided by the mass. Thus, a=F/m,a=F/m, or F=ma

Newton's 2nd law

forces cannot occur in isolation - To every action, there is an equal and opposite reaction

Newton's 3rd law

Kepler's First Law

The orbital paths of the planets are elliptical (not circular) with the sun at one focus

Kepler's Third Law

The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

Two otherwise isolated bodies of equal mass will orbit in which configurations as viewed from a fixed distant point?

They would orbit each other in identical but oppositely directed ellipses that share a common focus

Was it possible for the geocentric system of Ptolemy to explain the observed retrograde motion of the planets?

Yes, through a system of epicycles and deferents **The Ptolemaic system of epicycles and deferents survived for nearly 1300 years and was used as a practical, although complicated, system for calculation and prediction of planetary motions. It failed eventually on entirely different evidence but was able to explain and predict the retrograde motion of the planets.

Earth lay at the center of the universe and all other bodies moved around it - Aristotle

geocentric

an attractive force that acts between any two objects, directly proportional to mass of both bodies involved and inversely proportional to the square of the distance between them

gravitational force

The tendency of an object to keep moving at the same speed and in the same direction unless acted upon by a force

inertia

Orbit lies between the Sun and the Earth - Mercury and Venus

inferior "lower" planets

the planet is closest to Earth and moves past the Sun from east to west - in retrograde sense

inferior conjugation

According to Kepler's 2nd law a planet moves fastest in its orbit when...

it is closest to the sun

Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between their centers

law of gravity

How does orbital speed at aphelion compare to the speed at perihelion?

lower

A familiar measure of an object's inertia

mass

If Earth's orbit around the Sun were twice as large as it is now, the orbit would take

more than 2 times longer to transverse

If one star has twice the mass of the other, then the more massive star

moves more slowly than the less massive star.

Galileo's observations of Venus demonstrated that Venus must be

orbiting the sun

Escape velocity is the speed required to:

overcome the gravitational pull of an object

Motion in the eastward sense

prograde(direct) motion

According to Kepler's third law, the square of the planet's period in years is:

proportional to the cube of its semimajor axis in A.U.

Motion in the backward (westward) sense

retrograde motion

Planets near opposition

rise in the east

An object's velocity includes both:

speed AND direction in space

Orbit lies outside of Earth's - Mars, Jupiter, and Saturn

superior "higher" planets

the planet is farthest from the Earth and passes the sun in the opposite-prograde direction

superior conjugation

According to Newton, planets orbit in ellipses with what at the two foci?

the center of mass and nothing

the three laws derived by Kepler describing the motion of the planets around the Sun

Law of planetary motion

moving object will move forever in a straight line, unless some external force—a push or a pull—changes its speed or direction of motion

Newton's 1st law

A measure of the flatness of an ellipse, equal to the distance between the two foci divided by the length of the major axi

eccentricity

The average distance from Earth to the sun is

1 AU

Who proposed the geocentric view that was accepted and used for more than 18 centuries?

Aristotle

In what way did Newton improve Kepler's laws?

He discovered the dependence on mass in the third law.

Model in which the Earth and planets revolve around the Sun at the center of the Solar System - Copernicus

Heliocentric Model

For an object in a circular orbit, how does the velocity depend on the radius of the orbit?

It is inversely proportional to the square root of the radius.

The orbit of a planet around the Sun is an ellipse, with the center of mass of the planet-Sun system at one focus

Kepler's 1st law after Newton

the basic laws of motion, postulated by Newton, which are sufficient to explain and quantify virtually all of the complex dynamical behavior found on Earth and elsewhere in the universe

Newtonian mechanics

Kepler's third law is best expressed as ________.

P2 ~ a3

a model used to explain the retrograde motion of the planets - planet moves in a circle known as an epicycle, while the epicenter moves around the larger circle called the deferent (stationary Earth remains at the center of this). These movements combine to make retrograde motion.

Ptolemy's Model

How does Newton's Universal Law of Gravitation explain Kepler's laws?

Universal gravitation implies that the planets further from the Sun will move more slowly than the planets closer to the Sun (Kepler's third law); Universal gravitation implies that when a planet is closer to the Sun in its orbit, it will move faster than when it is farther from the Sun (Kepler's second law)

An accurate sketch of Jupiter's orbit around the Sun would show

a nearly perfect circle

shift in the observed direction to a star, caused by Earth's motion perpendicular to the line of sight - the direct evidence of Earth's motion; 1st proof that Earth revolves around the sun; James Bradley

aberration of starlight

rate of change of the velocity of an object—speeding up, slowing down, or simply changing direction

acceleration

Kepler's Second Law

an imaginary line connecting the sun to any planet sweeps out equal areas of the ellipse in equal intervals of time

Which of the following is NOT true about the solar system model of Copernicus? a. Its central organizing principle and primary attraction to Copernicus were that it was simpler to comprehend than the Ptolemaic model. b. It used elliptical orbits for the motions of the planets.It could explain apparent retrograde motion by showing that fast-moving inner planets "passed" slower outer planets as they went around the Sun. c. It used an earlier Greek idea that placed the Sun at the center of the solar system. d. It was not widely accepted and was not even published until the year he died.

b. It used elliptical orbits for the motions of the planets.It could explain apparent retrograde motion by showing that fast-moving inner planets "passed" slower outer planets as they went around the Sun.

During the Dark Ages (roughly from the 5th to the 10th century A.D.), turmoil in Europe largely halted the progress of Western science. Which culture provided the vital link between the astronomy of ancient Greece and that of medieval Europe during this time? a. North American b. Muslim c. South American d. Chinese

b. Muslim **For six centuries, Islamic astronomy flourished and grew, preserving and augmenting the knowledge of the Greeks. Its influence on modern astronomy is subtle but quite pervasive

Which of the following was not one of the discoveries made by Galileo? a. Several moons orbit Jupiter. b. The shape of an orbit is an ellipse. c. The Moon has mountains, valleys, and craters. d. The Sun has spots and rotates.

b. The shape of an orbit is an ellipse.

Kepler's second law of planetary motion states that a planet in orbit around the Sun will do which of the following? a. move equal distances in equal times b. sweep out equal areas in equal times c. eventually fall into the Sun d. always move in a circle

b. sweep out equal areas in equal times

If the distance between two asteroids is doubled, the gravitational force they exert on each other will:

be one fourth as great

Which concept was NOT a part of Kepler's Laws of Planetary Motion? a. The square of the planet's period is equal to the cube of its average distance. b. All planetary orbits are ellipses. c. A planet must move fastest in its orbit at perihelion.

c. A planet must move fastest in its orbit at perihelion.

showing the motion of a ball near Earth's surface, depicts how gravity

causes the ball to accelerate downward

A major flaw in Copernicus's model was that it still had

circular orbits