Solved: The ratio of circumference to diameter for

Make up a multiple-choice question to check a classmate’s understanding of the effect of gravity on time.

Problem 1RQ What is the principal difference between the theory of special relativity and the theory of general relativity?

Problem 3E Provide a classical explanation for an astronaut in an orbiting spacecraft experiencing no net force (as measured by a weighing scale), even though the astronaut is in the grips of Earth gravity.

Problem 1E What is different about the reference frames that apply to special relativity and to general relativity?

Problem 2RQ In a spaceship accelerating at ?g?, far from Earth’s gravity, how does the motion of a dropped ball compare with the motion of a ball dropped at Earth’s surface?

Problem 3RQ Exactly what is? quivalent? in the principle of equivalence?

An astronaut is provided a “gravity” when the spaceship’s engines are activated to accelerate the ship. This requires the use of fuel. Is there a way to accelerate and provide “gravity” without the sustained use of fuel? Discuss, perhaps using ideas from Chapter 8.

Problem 4RQ Compare the bending of the paths of baseballs and photons by a gravitational field.

Problem 5E In a spaceship far from the reaches of gravity, under what conditions could you feel as if the spaceship were stationary on Earth’s surface?

Problem 5RQ Why must the Sun be eclipsed to measure the deflection of starlight passing near the Sun?

Problem 6E In his famous novel ?Journey to the Moon, Jules Verne stated that occupants in a spaceship would shift their orientation from up to down when the ship crossed the point where the Moon’s gravitation became greater than Earth’s. Is this correct? Defend your answer.

Problem 6RQ What is the effect of strong gravitation on measurements of time?

Problem 7E What happens to the separation distance between two people if they both walk north at the same rate from two locations on Earth’s equator? And just for fun, where in the world is a step in every direction a step south?

Problem 7RQ Which runs slower, a clock at the top of the tallest skyscraper in Chicago or a clock on the shore of Lake Michigan?

Problem 8E We readily note the bending of light by reflection and refraction, but why are we not aware of the bending of light by gravity?

Problem 8RQ How does the frequency of a particular spectral line observed in sunlight compare with the frequency of that line observed from a source on Earth?

Problem 9E Light ?does bend in a gravitational field. Why is this bending not taken into consideration by surveyors who use laser beams as straight lines?

If we view events occurring on a star that is collapsing to become a black hole, do we see time speeded up or slowed down?

Problem 10E Why do we say that light travels in straight lines? Is it strictly accurate to say that a laser beam provides a perfectly straight line for purposes of surveying? Explain.

Problem 10RQ Of all the planets, why is Mercury the best candidate for finding evidence of the relationship between gravitation and space?

Problem 11E Your friend says that light passing the Sun is bent whether or not Earth experiences a solar eclipse. Do you agree or disagree, and why?

Problem 11RQ In what kind of gravitational field are Newton’s laws valid?

Problem 12E In 2004, when Mercury passed between the Sun and Earth, sunlight was not appreciably bent as it passed Mercury. Why?

Problem 12RQ A measuring stick placed along the circumference of a rotating disk will appear contracted, but if it is oriented along a radius, it will not. Explain.

Problem 13E A setting Sun is seen as distorted on Earth, but not by astronauts on the Moon. What causes this distortion?

Problem 14RQ What effect does mass have on spacetime?

The ratio of circumference to diameter for measured circles on a disk equals \(\pi\) when the disk is at rest, but not when the disk is rotating. Explain.

Problem 14E At the end of 1 s, a horizontally fired bullet drops a vertical distance of 4.9 m from its otherwise straight-line path in a gravitational field of 1 ?g?. By what distance would a beam of light drop from its otherwise straight-line path if it traveled in a uniform field of 1 ?g? for 1 ?s?? For 2 ?s??

Problem 15E Light changes its energy when it “falls” in a gravitational field. This change in energy is not evidenced by a change in speed, however. What is the evidence for this change in energy?

Problem 16E Would we notice a slowing down or speeding up of a clock if we carried it to the bottom of a very deep well?

Problem 17E If we witness events occurring on the Moon, where gravitation is weaker than on Earth, would we expect to see a gravitational red shift or a gravitational blue shift? Explain.

What occurs in the surrounding space when a massive object undergoes a change in its motion?

Problem 16RQ A star 10 light-years away explodes and produces gravitational waves. How long will it take these waves to reach Earth?

Problem 17RQ Why are gravitational waves so difficult to detect?

Problem 18E Armed with highly sensitive detection equipment, you are in the front of a railroad car that is accelerating forward. Your friend at the rear of the car shines green light toward you. Do you find the light to be red-shifted (lowered in frequency), blue-shifted (increased in frequency), or neither? Explain. (?Hint: Think in terms of the principle of equivalence. What is your accelerating railroad car equivalent to?)

Problem 18RQ Does Einstein’s theory of gravitation invalidate Newton’s theory of gravitation? Explain.

Problem 19E Why will the gravitational field intensity increase on the surface of a shrinking star?

Problem 20E Will a clock at the equator run slightly faster or slightly slower than an identical clock at one of Earth’s poles?

Problem 19RQ Is Newtonian physics adequate to get a rocket to the Moon?

Problem 20RQ How does Newtonian physics link with quantum theory and relativity theory?

Problem 21E Do you age faster at the top of mountain or at sea level?

Problem 22E Splitting hairs, should a person who worries about growing old live at the top or at the bottom of a tall apartment building?

Problem 23E Which would run slower, a clock at the center of a rotating space habitat or one at the edge? Or would there be no difference?

Problem 24E Prudence and Charity are twins raised at the center of a rotating kingdom. Charity goes to live at the edge of the kingdom for a time and then returns home. Which twin is older when they rejoin? (Ignore any time-dilation effects associated with travel to and from the edge.)

Problem 25E Splitting hairs, if you shine a beam of colored light to a friend above in a high tower, will the color of light your friend receives be the same color you send? Explain.

Problem 26E Is light emitted from the surface of a massive star red-shifted or blue-shifted by gravity?

Problem 27E From our frame of reference on Earth, objects slow to a stop as they approach black holes in space because time gets infinitely stretched by the strong gravity near the black hole. If astronauts accidentally falling into a black hole tried to signal back to Earth by flashing a light, what kind of “telescope” would we need to detect the signals?

Problem 28E Would an astronaut falling into a black hole see the outside universe red-shifted or blue-shifted?

Problem 29E How can we “observe” a black hole if neither matter nor radiation can escape from it?

Problem 31E Why does the gravitational attraction between the Sun and Mercury vary? Would it vary if the orbit of Mercury were perfectly circular?

Problem 30E Should it be possible in principle for a photon to circle a very massive star?

Problem 32E Your friend whimsically says that at the North Pole, a step in any direction is a step south. Do you agree?

In the astronomical triangle shown in Figure 36.14, with sides defined by light paths, the sum of the interior angles is more than \(180^\circ\). Is there any astronomical triangle whose interior angles sum to less than \(180^\circ\)?

Problem 34E Do binary stars (double-star systems that orbit about a common center of mass) radiate gravitational waves? Why or why not?

Problem 35E Given the possible sources of gravitational waves in the universe, would you expect them to have short wavelengths or long?

Based on what you know about the emission and absorption of electromagnetic waves, suggest how gravitational waves are emitted and how they are absorbed. (Scientists seeking to detect gravitational waves must arrange for them to be absorbed.)

Problem 37E Comparing Einstein’s and Newton’s theories of gravitation, how can the correspondence principle be applied?

Problem 38E Current findings suggest that the universe is flat. What is an implication of this finding?

Problem 39E Make up a multiple-choice question to check a classmate’s understanding of the principle of equivalence.

What is the principal difference between the theory of special relativity and the theory of general relativity?

In a spaceship accelerating at g, far from Earth’s gravity, how does the motion of a dropped ball compare with the motion of a ball dropped at Earth’s surface?

Principle of Equivalence Exactly what is equivalent in the principle of equivalence?

Compare the bending of the paths of baseballs and photons by a gravitational field.

Why must the Sun be eclipsed to measure the deflection of starlight passing near the Sun?

What is the effect of strong gravitation on measurements of time?

Which runs slower: a clock at the top of the tallest skyscraper in Chicago or a clock on the shore of Lake Michigan?

How does the frequency of a particular spectral line observed in sunlight compare with the frequency of that line observed from a source on Earth?

If we view events occurring on a star that is collapsing to become a black hole, do we see time speeding up or slowing down?

Of all the planets, why is Mercury the best candidate for finding evidence of the relationship between gravitation and space?

For what kind of gravitational field is Newton’s law of gravity valid?

A measuring stick placed along the circumference of a rotating disk will appear contracted, but if it is oriented along a radius, it will not. Explain.

The ratio of circumference to diameter for measured circles on a disk equals \(\pi\) when the disk is at rest, but not when the disk is rotating. Explain. Text Transcription: pi

What effect does mass have on spacetime?

A star 10 light-years away explodes and produces gravitational waves. How long will it take these waves to reach Earth?

What occurs in the surrounding space when a massive object undergoes a change in its motion?

Why are gravitational waves so difficult to detect?

Does Einstein’s theory of gravitation invalidate Newton’s theory of gravitation? Explain.

Is Newtonian physics adequate to get a rocket to the Moon?

How does Newtonian physics link with quantum theory and relativity theory?

What is different about the reference frames that apply to special relativity and to general relativity?

An astronaut awakes in her closed capsule, which actually sits on the Moon. Can she tell whether her weight is the result of gravitation or of accelerated motion? Explain.

In a spaceship far from the reaches of gravity, under what conditions could you feel as if the spaceship were stationary on Earth’s surface?

Provide a classical explanation for an astronaut in an orbiting spacecraft experiencing no net force (as measured by a weighing scale), even though the astronaut is in the grips of Earth gravity.

What happens to the separation distance between two people if they both walk north at the same rate from two locations on Earth’s equator? And, just for fun, where in the world is a step in every direction a step south?

We readily note the bending of light by reflection and refraction, but why aren’t we aware of the bending of light by gravity?

Light does bend in a gravitational field. Why isn’t this bending taken into consideration by surveyors who use laser beams as straight lines?

Your friend says that light passing the Sun is bent whether or not Earth experiences a solar eclipse. Do you agree or disagree, and why?

Why do we say that light travels in straight lines? Is it strictly accurate to say that a laser beam provides a perfectly straight line for purposes of surveying? Explain.

In 2004, when Mercury passed between the Sun and Earth, sunlight was not appreciably bent as it passed Mercury. Why?

A setting Sun is seen as distorted on Earth, but not by astronauts on the Moon. What causes this distortion? (Why could this question have been asked in Chapter 28?)

At the end of 1 s, a horizontally fired bullet drops a vertical distance of 4.9 m from its otherwise straight-line path in a gravitational field of 1 g. By what distance would a beam of light drop from its otherwise straight-line path if it traveled in a uniform field of 1 g for 1 s? For 2 s?

Light changes its energy when it “falls” in a gravitational field. This change in energy is not evidenced by a change in speed, however. What is the evidence for this change in energy?

Would we notice a slowing down or speeding up of a clock if we carried it to the bottom of a deep well?

If we witness events occurring on the Moon, where gravitation is weaker than on Earth, would we expect to see a gravitational red shift or a gravitational blue shift? Explain.

If Earth were a perfect sphere, would a clock at the equator run slightly faster or slightly slower than an identical clock at one of Earth’s poles?

Why will the gravitational field intensity increase on the surface of a shrinking star?

Do you age faster at the top of a mountain or at the mountain’s base

Splitting hairs, should a person who worries about growing old relative to the “man on the street” live at the top or at the bottom of a tall apartment building?

Which would run slower: a clock at the center of a rotating space habitat or one at the edge? Or would there be no difference?

Splitting hairs, if you shine a beam of colored light to a friend above in a high tower, will the color of light your friend receives be the same color you send? Explain.

Is light emitted from the surface of a star red-shifted or blue-shifted by gravity?

Would an astronaut falling into a black hole see the outside universe red-shifted or blue-shifted?

How can we “observe” a black hole if neither matter nor radiation can escape from it?

Should it be possible in principle for a photon to circle a very massive star?

Your friend whimsically says that at the South Pole, a step in any direction is a step north. Do you agree?

Why does the gravitational attraction between the Sun and Mercury vary? Would it vary if the orbit of Mercury were perfectly circular?

In the astronomical triangle shown in Figure 36.14, with sides defined by light paths, the sum of the interior angles is greater than \(180^{\circ}\). Is there any astronomical triangle whose interior angles sum to less than \(180^{\circ}\)?

Do binary stars (double-star systems that orbit about a common center of mass) radiate gravitational waves? Why or why not?

Given the possible sources of gravitational waves in the universe, would you expect them to have short wavelengths or long?

Based on what you know about the emission and absorption of electromagnetic waves, suggest how gravitational waves are emitted and how they are absorbed. (Scientists seeking to detect gravitational waves must arrange for them to be absorbed.)

Comparing Einstein’s and Newton’s theories of gravitation, how can the correspondence principle be applied?

Current findings suggest that the universe is flat. What is an implication of this finding?

Make up a multiple-choice question to check a classmate’s understanding of the principle of equivalence.

Make up a multiple-choice question to check a classmate’s understanding of the effect of gravity on time.

An astronaut is provided a “gravity” when the spaceship’s engines are activated to accelerate the ship. This requires the use of fuel. Is there a way to accelerate and provide “gravity” without the sustained use of fuel? Discuss, perhaps using ideas from Chapter 8.

In his famous novel Journey to the Moon, Jules Verne stated that occupants in a spaceship would shift their orientation from up to down when the ship crossed the point where the Moon’s gravitation became greater than Earth’s. Is this correct? Discuss.

Armed with highly sensitive detection equipment, you are in the front of a railroad car that is accelerating forward. Your friend at the rear of the car shines green light toward you. Do you find the light to be red-shifted (lowered in frequency), blue-shifted (increased in frequency), or neither? Explain. (Hint: Think in terms of the principle of equivalence. What is your accelerating railroad car equivalent to?)

Prudence and Charity are twins raised at the center of a rotating kingdom. Charity goes to live at the edge of the kingdom for a time and then returns home. Discuss which twin is older when they rejoin. (Ignore any time dilation effects associated with travel to and from the edge.)

From our frame of reference on Earth, objects slow to a stop as they approach black holes in space because time gets infinitely stretched by the strong gravity near the black hole. If astronauts accidentally falling into a black hole tried to signal back to Earth by flashing a light, what kind of “telescope” would we need to detect the signals?