Foundations of Astronomy 13e Chapter 5 review Questions

How does the first postulate of special relativity imply the second postulate?

The first postulate states that it is impossible in a closed craft to determine your true motion. If the speed of light were not constant, you could use the determination of the speed of light as a velocity meter. Therefore, the speed of light must be constant for all observers in uniform motion.

According to Aristotle, if earth and water were displaced then they would return naturally to their proper place. Today, what do we call this Aristotelean Natural Motion?

Today, natural motion of Aristotle's time is known as the force of gravity.

How many accelerators does a car have?

Acceleration is a change (generally, an increase) in velocity due to a force acting upon a mass while deceleration is a decrease in velocity due to a force acting upon a mass.

If you drop a feather and a steel hammer at the same moment, they should hit the ground at the same instant, Why doesn't this work on Earth, and why does it work on the moon? Will it work on Phobos, a moon of mars?

Air resistance. On Earth the air resistance on the feather is much greater than it is on the hammer. This resistance slows the feather, while the hammer accelerates downward. On the moon, there is no atmosphere, and hence no air resistance, and both the feather and hammer continue to accelerate as they fall.

Why would Aristotle's explanation of gravity not work if Earth is not the center of the universe?

Aristotle taught that things composed of earth and/or water naturally moved toward the center of the universe. If Earth were not at the center, all of these things would be pulled off Earth and toward the center of the universe.

If a planet were to migrate inward toward the Sun, would its orbital speed increase, decrease, or stay the same? Would its angular momentum change? Which of Kepler's laws or newton's versions of Kepler's laws does this scenario describe?

As a planet migrated towards the Sun, its orbital speed would increase while its angular momentum is conserved (stays the same). This scenario describes Kepler's second law, which states that a planet moves faster when it's near the Sun and slower when it's further away.

You put your astronomy textbook and your No. 2 pencil on a ceramic tile floor, and you blow on each. Which has more inertia, the textbook, the pencil, or neither? Why? Which has more momentum? Why?

Assuming that the book does not move and the pencil rolls when acting upon by the force of blowing, the book has more inertia, or more resistance to a change in motion. However, the pencil has more momentum, which is a measure of a body's motion and is a product of mass and velocity. Since the book has zero velocity, the book has zero momentum, while the pencil has a momentum > 0.

How is gravity related to acceleration? Are all accelerations the result of gravity?

Gravity is the force that tells a mass how to accelerate. According to general relativity, all masses cause curvature of the space around them, and the larger the mass, the more severe the curvature - so all accelerations are the result of gravity.

Why can't you leave earth's gravitational field when jumping vertically?

I cannot leave Earth's gravity field when jumping because I do not jump fast enough to exceed the escape velocity of Earth (11.2 km/s).

Near a massive planet, is gravitational acceleration large or small? Is space strongly curved or not? What about near a small marble?

If the object in question is a large galaxy, gravity is high because the great amount of mass is causing a large curvature in space-time and the resulting accelerations would be slow. Conversely, because the mass of a small marble is low, space-time is not highly curved, gravity is low, resulting in slow accelerations.

What is the difference between mass and weight?

Mass is a measure of how much matter an object has. Weight is a measure of how strongly gravity pulls on that matter.

Why did Newton conclude that some force had to pull the moon toward Earth?

Newton knew that objects move in a straight line at constant velocity, unless acted upon by an outside force (Newton's first law). The moon, however, followed a circular path around Earth. Therefore, some force must constrain the moon to move along a circular path.

In what conditions do newton's laws of motion and gravity need to be modified?

Newton's laws of motion and gravity do not apply to open orbits.

Which of Kepler's or Newton's laws best describes Aristotelean violent motions?

Newton's second law of motion (F = ma) best describes "violent motions". The acceleration of a particle is dependent upon forces acting upon the particle.

You weigh 100 pounds, your friend weighs 200 pounds, and you are in an arm wrestling contest with each other. Neither person is winning, but each of you is struggling to push the other's forearm over to the tabletop. Which of Kepler's or Newton's laws applies to this scenario and why? Now in one swift motion you plant your friends forearm on the table, winning the contest. Which of Kepler's or Newton's laws applies to this motion and why?

Newton's third law (forces must occur in pairs directed in opposite directions) is most applicable to the scenario. The force that I am exerting is equal but opposite to the force that my friend is exerting. When I succeed in pushing my friends forearm to the table, Newton's second law (F=ma) applies because the force (F) that I applied to the mass (m) of my friend's arm was sufficient to accelerate (a) his or her forearm to the table.

Why did newton conclude that gravity has to be mutual and universal?

Newton's third law stated that for every action there is an equal and opposite reaction. If one object pulls on a second, the second must also pull on the first with an equal but opposite force. Therefore, objects of any mass would attract any other object of mass.

What is the difference between speed and velocity?

Speed is the rate at which an object is moving. Velocity is the vector quantity that expresses both the rate and direction an object is moving.

How do planets orbiting the Sun and skaters doing a spin both conserve angular momentum?

The angular momentum of a planet is conserved because it moves faster when it is near perihelion than when it is near aphelion. A skater's angular momentum is conserved because she will spin faster when her arms and legs are drawn in near her torso and spin less rapidly when her arms are extended outward horizontally.

According to Kepler's first law, planets move in elliptical orbits. Why is that considered accelerated motion? According to newton, what is the force causing that acceleration?

The attractive force that Newton is referring to is gravity and the object (planets) experiencing the force of gravity are in motion (orbiting).

An astronaut is in space with a baseball and a bowling ball. The astronaut gives both objects an equal push in the same direction. Does the baseball have the same inertia as the bowling ball? Why? Does the baseball have the same acceleration as the bowling ball from the push? Why? If both balls are traveling at the same speed, does the baseball have the same momentum as the bowling ball?

The baseball would have the same inertia as the bowling ball because both have equal motion and will continue until another force acts upon it. The baseball would have greater acceleration than the bowling ball because the bowling ball has the same force acting on a greater mass. If both balls are traveling at the same velocity, the bowling ball would have more momentum due to its higher mass.

You are at a red light in your car. The red light turns green, and you put your car in first gear and step on the gas pedal. The speedometer changes from 0 to 10 to 20 mph in 3 seconds. In this span of time, did the car accelerate or decelerate, and in which direction? Did the car increase in speed, decrease in speed, or travel at the same speed, and in which direction?

The car accelerated in the forward direction, which is saying that it increased in speed in the forward direction.

A car is on a circular off ramp of an interstate and is traveling at exactly 25 mph around the curve. Does the car have velocity? Does the car have acceleration? Is the car decelerating?

The car has a velocity of 25 mph. As it turns to stay on the circular path, the car is being acted upon by two forces: one force that is pushing it away from the center of the circle (centripetal force) and equal but opposite force that is pushing it towards the center of the circle (friction between the tires and the road). Because these forces oppose one another, the car is neither accelerating nor decelerating.

Where is the center of mass of your body?

The center of mass of a human is always changing because the shape changes with position as well as with differences in physique. In general, the center of mass of a standing human body is within the core of the body, but is generally located slightly higher in men and slightly lower in women.

What is the center of mass of two bodies? Where is the center of mass of the Earth-Moon system?

The center of mass of the Earth-moon system is the balance point for the two objects. The center of mass is located along the line from the center of Earth to the center of the moon and at a distance of about 4,708 km from the center of Earth.

When you ride a fast elevator upward, you feel slightly heavier as the trip begins and slightly lighter as the trip ends. How is this phenomenon related to the equivalence principle?

The equivalence principle states that an observer cannot distinguish between a force due to acceleration and a force due to gravity. When the elevator begins to move, you are accelerated upward with increasing speed, and you feel an increase in your apparent weight. Since you can only determine that your apparent weight has increased and not the cause of the increase, it is impossible to distinguish between a force due to acceleration and one due to gravity.

How does the concept of a field explain action at a distance? name another kind of field also associated with action at a distance.

The field was a representation of the influence that a mass could have on another object. The presence of the mass would affect the field which spreads out in all directions from the mass. Any other object with mass placed in the field would experience a force at some distance as a result of its interaction with the field. Examples of other interactions described as using fields include magnetic and electric interactions.

Why can't a spacecraft go "beyond Earth's gravity"?

The force of gravity decreases as the inverse of the distance-squared. This force drops to zero at a distance of infinity. Therefore, Earth will always pull on a spacecraft, regardless of its distance from Earth.

You are sitting next to a person who has twice as much weight. You get up and move one seat over, doubling your distance from them. Did the gravitational force between you increase, decrease, or stay the same?

The gravitational attraction decreased because the gravitational force is inversely proportional to the square of the distance between two masses.

You are sitting next to a person who has twice as much weight as you do. A friend comes by and gives you a marshmallow and you eat it. Did your gravitational force between you increase, decrease, or stay the same?

The gravitational force to my neighbor would increase slightly (as would his force on me) due to increasing the mass of the system because the gravitational force is proportional to the product of the masses involved.

If you hold this textbook out at shoulder height and let go, at the instant you let go, does the book have potential energy? Kinetic energy?

The moment I let go, the book has potential energy due to its position within Earth's gravitational field. However, it does not have kinetic energy, which because it is not yet moving and therefore cannot affect change on another object.

Today at the beach you see the highest of all high tides in the last month, You see the Moon in the daytime sky. What is the most likely Moon phase?

The mostly likely Moon phase is waxing crescent.

According to the principles of Aristotle, what part of the motion of a baseball pitched across home plate is natural motion? What part is violent motion?

The natural motion of the baseball is its entire flight, beginning at the instant that it leaves the pitcher's hand. The violent motion is that motion of the ball while the pitcher is winding up and throwing the ball. The violent motion ends when the ball is released.

Why is the period of an open orbit undefined?

The period of an orbit is the time required for the object to complete one revolution around the parent object. In an open orbit, the object never completes a revolution because it will not return.

Today, what do we call Aristotelean Violent motion?

Today, the violent motion of Aristotle's time is known as a force that acts against gravity.

An astronaut working in space near the International Space Station says she feels weightless. What does she mean? Does the astronaut not have weight?

We feel weight on Earth as the force that Earth exerts on us gravitationally as our feet press on the floor. In orbit, both the very massive spacecraft and the low mass astronaut are falling toward Earth, and there is no solid surface pushing back on them. Since they are really falling around Earth, free of all forces except gravity, the term free-fall would be more accurate than "weightless."

When a person says he gained weight, does he mean that he gained in mass, gravity, or both mass and gravity?

When a person says he gained weight, he means that he gained mass.

Balance a pencil lengthwise on the side of your finger. Where is the center of mass? Balance a pencil widthwise (for example, on the eraser side) on your finger. Where is the center of mass? Is the center of mass a place, sphere, circle, point, or a line?

When balancing a pencil lengthwise on the side of a finger, the center of mass is a point located within the pencil where it rests on my finger. When balancing a pencil widthwise, the center of mass is located at the center of the length of the pencil. In that instance, the center of mass is a line.

You have the same mass as a person sitting next to you. Are you gravitationally attracted to him? If so , why don't you instantly zoom over and stick to him? Is the attraction mutual? If not, why not?

Yes, because we both have mass our bodies are gravitationally attracted to one another (i.e., mutual). However because our mass is fairly small, this mutual gravitational attraction is very small.

You are sitting next to a person who has twice as much weight. Are you gravitationally attracted to them? If so, is it twice as much as their attraction to you? if not, why not?

Yes, my mass would be gravitationally attracted to her. Our gravitational attraction is equal because the force of gravity is proportional to the product of our two masses, not dependent just on the other mass.

From your knowledge of general relativity, would you expect radio waves from distant galaxies to be deflected as the pass near the sun? Why or why not?

Yes. Radio waves are a form of electromagnetic radiation just like visible light. Since the gravitational force of the sun bends light, radio waves should be bent as well.