Chapter 1: The History of Astronomy, Kepler, and Newton

A circular orbit would have an eccentricity of

0.

Consider again the diagrams from Parts D and E, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions (A-D) from left to right based on how fast the asteroid is moving at each position.

Same answers as before.

How does the parallax of a nearby object compare to that of an object farther away?

The nearby object exhibits a larger parallax than the farther object.

Which of the following is NOT one of Newton's Laws of Motion?

The orbital paths of the planets are elliptical (not necessarily circular), with the Sun at one focus.

Which of the following was NOT one of the discoveries made by Galileo?

The shape of a planet's orbit is an ellipse.

Each of the four diagrams below represents the orbit of the same asteroid, but each one shows it in a different position along its orbit of the Sun. Imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. Rank the positions based on the area that would be swept out by a line drawn between the Sun and the asteroid during the one-week period.

Trick question again, place all diagrams into the middle slot between largest and smallest.

According to Newton's second law, if you double the force acting on a body, the acceleration will double.

True

According to Newton's third law, when the Voyager probes passed Jupiter in 1979, they exerted exactly the same force on Jupiter as the giant planet did on them.

True

Increasing the baseline will increase the parallax angle.

True

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

a nearly perfect circle.

The geocentric model, in all of its complexity, survived scientific scrutiny for almost 1,400 years. However, in modern astronomy, scientists seek to explain the natural and physical world we live in as simply as possible. The complexity of Ptolemy's model was an indicator that his theory was inherently flawed. Why, then, was the geocentric model the leading theory for such a long time, even though the heliocentric model more simply explained the observed motions and brightness of the planets?

- The geocentric model conformed to both the philosophical and religious doctrines of the time. - The heliocentric model did not make noticeably better predictions than the geocentric model. - Ancient astronomers did not observe stellar parallax, which would have provided evidence in favor of the heliocentric model. - From Earth, all heavenly bodies appeared to circle around a stationary Earth.

Copernicus believed the Earth was the center of all celestial motion.

False

In Ptolemy's geocentric model, the planet's motion along its deferent is all that is needed to understand retrograde motion.

False

Kepler's third law allows us to find the average distance to a planet from observing its period of rotation on its axis.

False

Copernicus's heliocentric model and Ptolemy's geocentric model were each developed to provide a description of the solar system. Both models had advantages that made each an acceptable explanation for motions in the solar system during their time. Sort each statement according to whether it is an advantage of the heliocentric model, the geocentric model, or both.

Geocentric: - Rooted in widely accepted religious beliefs regarding Earth's place in the Universe. Heliocentric: - Explained planetary motions and brightness changes most simply. Both: - Planetary orbits and motions based on Greek ideologies of perfect form and motion. - Predicted planetary positions accurately over relatively short time periods.

The force of gravity between two objects obeys which of the following relationships?

It is attractive and increases if their masses increase.

_____'s theories were based on the very accurate observations made by _____.

Kepler, Tycho Brahe

Consider again the diagrams from Part D, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions from left to right based on the distance the asteroid will travel during a one-week period when passing through each location.

Longest: When the asteroid is directly below the Sun. Second from Left: Slightly to the right of the sun. Second from Right: Top left of the diagram away from the Sun. Shortest: Farthest away from the sun but directly parallel to it.

Consider again the diagrams from Part A, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit from left to right based on the distance the comet travels when moving from Point 1 to Point 2.

Longest: Where the shaded part is directly left to the Sun. Second to Left: Where the labels 2 and 1 are slightly to the right, below the Sun. Second to Right: Where the labels 2 and 1 are slightly above the rightmost position near 40ish degrees on a circle. Shortest: Exactly to the right of the Sun, further away from it.

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

Lower

Each of the four diagrams below represents the orbit of the same comet, but each one shows the comet passing through a different segment of its orbit around the Sun. During each segment, a line drawn from the Sun to the comet sweeps out a triangular-shaped, shaded area. Assume that all the shaded regions have exactly the same area. Rank the segments of the comet's orbit from left to right based on the length of time it takes the comet to move from Point 1 to Point 2.

Place all four diagrams in the middle slot between longest and shortest, trick question.

Consider again the diagrams from Part A, which are repeated here. Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit from left to right based on the distance the comet travels when moving from Point 1 to Point 2.

Same positions as the last question.

What two measurable properties directly tell us the size and shape of a planet's orbit?

Semimajor axis and eccentricty.

According to Newton, the gravity of the _____ is needed to explain planetary orbits.

Sun

Kepler's second law of planetary motion states that a planet in orbit around the Sun will do which of the following?

Sweep out equal areas in equal times

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

The center of mass and nothing

If the distance between the centers of two objects doubles, what happens to the gravitational pull between them if the masses do not change?

The force will decrease to one-fourth its previous size.

Galileo's observations of the entire phase cycle of Venus proved that Ptolemy's epicycles could not be correct in keeping Venus between us and the Sun.

True

Kepler found the orbits of planets are ellipses, not circles.

True

The parallax shift for all stars is very small.

True

Copernicus' Heliocentric theory explains that

Venus retrogrades when she overtakes us at inferior conjunction.

According to Copernicus, the retrograde motion for Mars must occur

at opposition, when the Earth overtakes Mars and passes between Mars and the Sun.

Figure 1.17 in the textbook (Gravity), 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.

In Ptolemy's geocentric model, retrograde motion occurs when the planet is closest to us, on the inside portion of the

epicycle

According to Newton's laws, the planets orbit the Sun due to _____.

gravity

An asteroid with an orbit lying entirely inside Earth's

has an orbital semimajor axis of less than 1 AU.

Why would astronomers measure the parallax angle of a planet or star? What physical property of that object are they trying to determine?

its distance

Galileo's observations of the phases of Venus ________.

showed that Venus had to orbit the Sun and not the Earth

An Astronomical Unit (AU) is _________.

the average distance between the Sun and Earth

Two competing models attempt to explain the motions and changing brightness of the planets: Ptolemy's geocentric model and Copernicus' heliocentric model. Sort the characteristics according to whether they are part of the geocentric model, the heliocentric model, or both solar system models.

Geocentric: - This model is Earth-centered - Retrograde motion is explained by epicycles. Heliocentric: - This model is Sun-centered - Retrograde motion is explained by the orbital speeds of planets. Both: - Epicycles and deferents help explain planetary motion. - Planets move in circular orbits and with uniform motion. - The brightness of a planet increases when the planet is closest to Earth.