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Chapter 38: Problem 61

You and a group of female and male friends stand outdoors at dusk watching the Sun set and noticing the planet Venus in the same direction as the Sun. An alien ship lands beside you at the same instant that you see the Sun explode. The aliens admit that earlier they shot a laser flash at the Sun, which caused the explosion. They warn that the Sun's explosion emitted an immense pulse of particles that will blow away Earth's atmosphere. In confirmation, a short time after the aliens land you notice Venus suddenly change color. You and your friends plead with the aliens to take your group away from Earth in order to establish the human gene pool elsewhere. They agree. Describe the conditions under which your escape plan will succeed. Be specific and use numbers. Assume that the Sun is 8 light-minutes from Earth and Venus is 2 light-minutes from Earth.

Short Answer

Expert verified
Escape within 2 minutes after seeing Venus change color.

Step by step solution

01

- Determine the Timing of Events

Understanding the timing of events is crucial. The Sun is 8 light-minutes from Earth, so it takes 8 minutes for any light or information to travel from the Sun to Earth. Venus is 2 light-minutes from Earth, meaning any light change from Venus indicates something that occurred 2 minutes prior.
02

- Laser Flash Timing

When you see the Sun explode, it means the event happened 8 minutes earlier. Suppose the aliens shot the laser exactly 8 minutes before you saw the Sun explode.
03

- Particle Emission Timing

The emission of particles would also take 8 minutes to become visible to you, as they traveled at the speed of light.
04

- Venus Color Change Timing

Venus changing color 2 minutes after the aliens landed implies a delay. Since the change is seen by you after 2 minutes, it must have occurred at Venus 2 minutes before. Therefore, the particles hit Venus 6 minutes after they left the Sun (8 - 2 = 6 minutes).
05

- Calculating Escape Time

Since particles take 8 minutes to reach Earth from the Sun, and you noticed the color change on Venus 6 minutes after the explosion, you have 2 minutes left before the particles reach Earth. You must escape within these 2 minutes.
06

- Summarize and Conclusion

You have exactly 2 minutes to evacuate Earth and escape before the particle storm arrives.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

speed of light
The speed of light is a fundamental constant in physics. It is the speed at which light and all other electromagnetic waves travel in a vacuum. This speed is approximately 299,792,458 meters per second, or about 300,000 kilometers per second.
In our scenario, light from the Sun takes 8 minutes to reach Earth because the Sun is 8 'light-minutes' away. This distance is calculated by multiplying the speed of light by the number of minutes light takes to travel from the Sun to Earth.
Since Venus is 2 light-minutes away, light from Venus reaches Earth in just 2 minutes.
  • Speed of light to Earth from the Sun: 8 light-minutes
  • Speed of light to Earth from Venus: 2 light-minutes
You can always use the speed of light to calculate the time it takes for light or information to travel across distances in space.
Understanding this helps us predict when events such as the Sun's explosion will be visible from Earth.
time delay
In space, time delay occurs because of the vast distances between objects. When we observe an event, we are actually seeing it as it happened in the past, not in real-time.
When you saw the Sun explode, it had already happened 8 minutes earlier because of the 8 light-minute distance. Similarly, changes on Venus observed from Earth happen 2 minutes before you see them, due to the 2 light-minute distance.
In our exercise:
  • The Sun exploded 8 minutes before you saw it.
  • The particle emission from the Sun also began 8 minutes before you noticed the explosion.
  • Venus changing color was noticed 2 minutes after the explosion, indicating a 6-minute travel time for particles to reach Venus.
Time delay is a fundamental consideration in astronomy and astrophysics, affecting how we interpret observations and timings.
By accounting for these delays, you can more accurately predict events and outcomes, like in this escape scenario.
particle emission
Particle emission refers to the release of particles from a source, such as the explosion of the Sun in this scenario. These particles travel through space, sometimes at high speeds, and can pose significant risks.
In this exercise:
  • The Sun's explosion emitted a pulse of particles traveling at the speed of light.
  • The particles took 8 minutes to travel the distance from the Sun to Earth.
  • The observation of Venus changing color indicated that these particles affected Venus 6 minutes after the explosion and 2 minutes before reaching Earth.
These particles can include protons, neutrons, and other subatomic particles, and in this case, they are strong enough to blow away Earth's atmosphere.
Understanding the properties and behavior of particle emissions is crucial for predicting the impact of astronomical events and planning any necessary responses.
In this situation, knowing the timing and speed of particle emissions allowed you to determine that you had only 2 minutes to execute your escape plan before Earth's atmosphere would be compromised.

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Most popular questions from this chapter

Sara Settlemyer is an intelligent layperson who carefully reads articles about science in the public press. She has the objections to relativity listed below. Respond to each of Sara's objections clearly, decisively, and politely- without criticizing her! (a) "Observer A says that observer B's clock runs slow, while \(\mathrm{B}\) says that A's clock runs slow. This is a logical contradiction. Therefore relativity should be abandoned." (b) "Observer A says that B's meter sticks are contracted along their direction of relative motion. B says that A's meter sticks are contracted. This is a logical contradiction. Therefore relativity should be abandoned." (c) "Anybody with common sense knows that travel at high speed in the direction of a receding light pulse decreases the speed with which the pulse recedes. Hence a flash of light cannot have the same speed for observers in relative motion. With this disproof of the Principle of Relativity, all of relativity collapses." (d) "Relativity is preoccupied with how we observe things, not with what is really happening. Therefore relativity is not a scientific theory, since science deals with reality." (e) "Relativity offers no way to describe an event without coordinates, and no way to speak about coordinates without referring to one or another particular reference frame. However, physical events have an existence independent of all choice of coordinates and reference frames. Therefore the special relativity you talk about in this chapter cannot be the most fundamental theory of events and the relation between events."

An unpowered rocket moves past you in the positive \(x\) direction at speed \(v^{\text {rel }}=0.9 c\). This rocket fires a bullet out the back that you measure to be moving at speed \(v_{\text {bullet }}=0.3 c\) in the positive \(x\) direction. With what speed relative to the rocket did the rocket observer fire the bullet out the back of her ship?

Two freight trains, each of mass \(6 \times 10^{6} \mathrm{~kg}\) (6 000 metric tons) travel in opposite directions on the same track with equal speeds of \(150 \mathrm{~km} / \mathrm{hr}\). They collide head-on and come to rest. (a) Calculate in joules the kinetic energy \((1 / 2) m v^{2}\) for each train before the collision. (Newtonian expression OK for everyday speeds!) (b) After the collision, the mass of the trains plus the mass of the track plus the mass of the roadbed plus the mass of the surrounding air plus the mass of emitted sound and light has increased by what number of milligrams?

The values of the masses in the reaction \(p+{ }^{19} F \rightarrow \alpha+{ }^{16} O\) have been determined by a mass spectrometer to have the values: $$ \begin{aligned} m(p) &=1.007825 u, \\ m(F) &=18.998405 u, \\ m(\alpha) &=4.002603 u, \\ m(O) &=15.994915 u . \end{aligned} $$ Here \(u\) is the atomic mass unit (Section 1.7). How much energy is released in this reaction? Express your answer in both kilograms and \(\mathrm{MeV}\).

Quite apart from effects due to the Earth's rotational and orbital motion, a laboratory reference frame on the Earth is not an inertial frame, as required by a strict interpretation of special relativity. It is not inertial because a particle released from rest at the Earth's surface does not remain at rest; it falls! Often, however, the events in an experiment for which one needs special relativity happen so quickly that we can ignore effects duc to gravitational accclcration. Considcr, for cxamplc, a proton moving horizontally at speed \(v=0.992 c\) through a 10 -m-wide detector in a laboratory test chamber. (a) How long will the transit through that detector take? (b) How far does the proton fall vertically during this time lapse? (c) What do you conclude about the suitability of the laboratory as an inertial frame in this case?
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