Question 1

An object is in an orbit caused by its gravitational attraction to the Sun. This orbit
A) must be an ellipse.
B) must be a parabola.
C) must be a hyperbola.
D) might be an ellipse, a parabola, or a hyperbola.

Accepted Answer

According to Kepler's first law, an object in orbit around the Sun follows an elliptical path with the Sun at one of the foci. However, depending on the energy and dynamics of the object, its orbit can also be parabolic or hyperbolic. Elliptical orbits are closed and bound, while parabolic and hyperbolic orbits are open and unbound, typically associated with objects just passing through the solar system.

Question 2

Which of these four questions arising from modern ideas of force and matter is one of the great unanswered questions of contemporary science?
A) Why do planets move in elliptical orbits?
B) Why are the inertial mass (defined in Newton's second law) and the mass used in his law of gravitation identical?
C) What is force?
D) Why is Mercury's orbit measurably different from that predicted by Newton's laws?

Accepted Answer

The equivalence of inertial mass and gravitational mass is a deep question that remains unanswered. It's fundamental to the equivalence principle, which underpins general relativity, but why this equivalence exists is not fully understood.

Question 3

In the years after Newton published his laws of motion, it was found that the observed positions of the planet Uranus did not match the predictions of Newton's theory. The reason for this turned out to be
A) the gravitational influence of a previously unknown planet.
B) the perturbing effects of previously unknown satellites (moons) of Uranus.
C) inaccuracies in the observations.
D) inaccuracies in Newton's laws (later corrected by general relativity).

Accepted Answer

The observed discrepancies in the orbit of Uranus were explained by the gravitational influence of Neptune, a planet that had not been discovered at the time Newton published his laws of motion.

Question 4

Who predicted the existence of the planet Neptune before it was discovered observationally?
A) Kepler and Brahe
B) Newton and Halley
C) Adams and Leverrier
D) Kepler and Galileo

Accepted Answer

Adams and Leverrier independently predicted the existence of Neptune based on mathematical calculations and irregularities in the orbit of Uranus, leading to its discovery.

Question 5

Which of these objects are MOST likely found to follow parabolic orbits?
A) small satellites of the outer planets
B) asteroids
C) none-all orbits have to be ellipses
D) comets

Accepted Answer

Comets are most likely to follow parabolic orbits when they are on their first approach to the Sun from the outer solar system, as they are not gravitationally bound to the Sun in a closed elliptical orbit.

Question 6

In the years after Newton published his laws of motion, it was found that the observed positions of the planet Uranus did not match the predictions of Newton's theory. The reason for this turned out to be the
A) perturbing effects of Jupiter and Saturn, whose masses at that time were not accurately known.
B) perturbing effect of Neptune, which at that time had not yet been discovered.
C) perturbing effect of Pluto, which at that time had not yet been discovered.
D) weakening of gravity with increasing distance from the Sun.

Accepted Answer

The observed discrepancies in the orbit of Uranus led to the prediction and subsequent discovery of Neptune. The perturbing effect was due to Neptune's gravitational influence, which had not been accounted for because Neptune had not yet been discovered at the time.

Question 7

What is the typical period of a parabolic orbit?
A) infinite; parabolic orbits do not close upon themselves
B) any; parabolic orbits can have any semimajor axis
C) much less than 1 year
D) much greater than 1 year

Accepted Answer

Parabolic orbits are open orbits, meaning an object on a parabolic trajectory will escape the gravitational pull of the body it orbits and not return, implying an infinite period.

Question 8

Which of these situations describes an acceptable path for a body gravitationally bound to the Sun?
A) parabolic path passing through the center of the Sun
B) circular path with the Sun on the circle
C) long ellipse, with the Sun at one focus
D) long ellipse, with the Sun at its center

Accepted Answer

In celestial mechanics, a body orbiting the Sun in a stable, bound orbit will follow an elliptical path with the Sun at one of the foci, according to Kepler's first law of planetary motion. Options A, B, and D do not describe stable orbits for a body gravitationally bound to the Sun.

Question 9

Which object was discovered after its position had been predicted by the application of Newtonian mechanics to the deviation in the motion of another planet?
A) minor planet Ceres
B) Uranus
C) Neptune
D) Pluto

Accepted Answer

Neptune was discovered after its position had been predicted based on the deviations observed in the orbit of Uranus. Mathematicians and astronomers used Newtonian mechanics to calculate where another planet might be, influencing Uranus's orbit, leading to the discovery of Neptune.

Question 10

Which object was discovered mathematically using Newton's laws before it was discovered observationally through the telescope?
A) Pluto
B) Mercury
C) Neptune
D) Uranus

Accepted Answer

Neptune was discovered mathematically before being observed through a telescope. Its existence was predicted based on irregularities in the orbit of Uranus that could not be explained by the known planets alone. The calculations of John Couch Adams and Urbain Le Verrier led to its discovery in 1846.

Question 11

How was the planet Neptune discovered?
A) Neptune was discovered by mathematical prediction using Newton's laws.
B) Neptune happened to pass close to Jupiter in the sky and was discovered by an astronomer studying Jupiter.
C) Neptune was discovered accidentally during a telescopic survey of the sky.
D) No one knows-Neptune has been known since ancient times.

Accepted Answer

Neptune was discovered as a result of mathematical predictions made using Newton's laws of motion and gravitation. Observations of irregularities in the orbit of Uranus led astronomers to predict the position of another planet, which was then observed through a telescope.

Question 12

The first major astronomical prediction of Newton's theory of gravitation to be confirmed by observation was the
A) return of Comet Halley.
B) supernova of 1572.
C) discovery of Pluto.
D) discovery of Neptune.

Accepted Answer

Newton's theory of gravitation predicted the return of Comet Halley, which was confirmed when the comet reappeared in 1758, as predicted by Edmond Halley using Newton's laws.

Question 13

What is a hyperbola?
A) straight line extending to infinity in one direction
B) long, skinny ellipse
C) infinitely long curve that never closes on itself
D) ellipse with equal major and minor axes

Accepted Answer

A hyperbola is an open curve, meaning it extends infinitely in two opposite directions and does not form a closed loop. Unlike ellipses, hyperbolas do not close back on themselves.

Question 14

What is the typical period of a hyperbolic orbit?
A) infinite; hyperbolic orbits do not close upon themselves
B) any; hyperbolic orbits can have any semimajor axis
C) much less than 1 year
D) much greater than 1 year

Accepted Answer

Hyperbolic orbits are open paths that result from objects passing by a celestial body with enough velocity to escape its gravitational pull, meaning they do not form closed loops and extend to infinity.

Question 15

A comet, originating in the solar system, is observed to have a hyperbolic orbit. What is MOST likely to have happened?
A) The comet always had such an orbit.
B) The comet was deflected from an elliptical orbit by close encounters with other bodies in the solar system.
C) The comet was decelerated by solar radiation.
D) The comet's circular orbit was changed by gravitational radiation.

Accepted Answer

Comets originally move in elliptical orbits around the sun. A hyperbolic orbit suggests that the comet's path was altered, most likely due to gravitational interactions with other bodies in the solar system, such as planets or larger asteroids. These encounters can significantly change a comet's velocity and trajectory, potentially converting an elliptical orbit into a hyperbolic one, which will eventually lead the comet to leave the solar system.

Question 16

Suppose that an object is discovered moving around the Sun once every 120 years. Which of these paths is a possible orbit for this object?
A) straight line
B) parabola
C) ellipse
D) hyperbola

Accepted Answer

An object orbiting the Sun with a period of 120 years follows an elliptical path, as per Kepler's laws of planetary motion.

Quiz 2: Gravitation and the Motion of the Planets

An object is in an orbit caused by its gravitational attraction to the Sun. This orbit

Which of these four questions arising from modern ideas of force and matter is one of the great unanswered questions of contemporary science?

In the years after Newton published his laws of motion, it was found that the observed positions of the planet Uranus did not match the predictions of Newton's theory. The reason for this turned out to be

Who predicted the existence of the planet Neptune before it was discovered observationally?

Which of these objects are MOST likely found to follow parabolic orbits?

In the years after Newton published his laws of motion, it was found that the observed positions of the planet Uranus did not match the predictions of Newton's theory. The reason for this turned out to be the

What is the typical period of a parabolic orbit?

Which of these situations describes an acceptable path for a body gravitationally bound to the Sun?

Which object was discovered after its position had been predicted by the application of Newtonian mechanics to the deviation in the motion of another planet?

Which object was discovered mathematically using Newton's laws before it was discovered observationally through the telescope?

How was the planet Neptune discovered?

The first major astronomical prediction of Newton's theory of gravitation to be confirmed by observation was the

What is a hyperbola?

What is the typical period of a hyperbolic orbit?

A comet, originating in the solar system, is observed to have a hyperbolic orbit. What is MOST likely to have happened?

Suppose that an object is discovered moving around the Sun once every 120 years. Which of these paths is a possible orbit for this object?