Question

Choose the best answer to each of the following. Explain your reasoning with one or more complete sentences. The amount of energy that would be needed to accelerate a large spaceship to a speed close to the speed of light is (a) about 100 times as much energy as is needed to launch the Space Shuttle; (b) more than the total amount of energy used by the entire world in a year; (c) more than the amount of energy that our Sun emits into space in a year.

Short answer

The best answer is (c) more than the amount of energy that our Sun emits into space in a year.

Step-by-step solution

Analyze Each Option

First, we need to understand the context of the question. The amount of energy needed to accelerate a spaceship close to the speed of light is enormous due to Einstein's theory of relativity. Let's consider each option in turn. Option (a): 100 times the energy of the Space Shuttle - This option seems too low considering the vast amount of energy required according to relativity. Option (b): More than the total amount of energy used worldwide in a year - This option is feasible as Earth's annual energy use is enormous, yet not as vast as cosmic levels. Option (c): More than the Sun's annual energy output - This would be an extremely large amount of energy, possibly more than could be practical with current or foreseeable technology.

Apply Relativistic Concepts

Using the theory of relativity, the energy required to reach speeds close to the speed of light increases astronomically due to the increase in relativistic mass. As the spaceship approaches light speed, the Lorentz factor approaches infinity, thus requiring infinite energy.

Eliminate Impractical Options

Considering the exponential increase of energy needed: - Option (a) can be eliminated since the required energy is far greater than 100 times the energy needed for a Space Shuttle launch. - While option (b) is plausible, option (c) involves colossal energy, potentially unrealistic but indicative of truly cosmic scales needed.

Select the Best Option

Although reaching exact real-world energy calculations is complex, we recognize the immense energy needs from relativity. Among the given options, Option (c) provides the most realistic perspective given our understanding of physics. Space travel close to light speed implies vast, potentially solar-level energy amounts.

Key concepts

Spaceship Acceleration

Accelerating a spaceship to incredible speeds is no simple task. Even the Space Shuttle requires enormous energy to launch into orbit. But when we venture into the realm of increasing a spaceship's speed close to the speed of light, we confront orders of magnitude greater in energy demands.

This is because acceleration doesn't scale linearly with energy input. As velocity increases, especially when approaching the speed of light, the energy required grows exponentially. To accelerate a spaceship to near-light speeds, we'd need energy far beyond our current capabilities.

Key factors in these calculations include:

• Thrust to overcome inertia.
• Fuel efficiency and capacity.
• Relativistic effects on mass and energy.

Each of these factors necessitates an astronomical amount of energy, highlighting the enormous challenge of extraterrestrial travel at relativistic speeds.

Theory of Relativity

Einstein's theory of relativity drastically changed our understanding of time and space. At its core, it posits that the laws of physics are the same for all non-accelerating observers. One fascinating consequence is the relationship between mass and energy, epitomized in the famous equation, \(E=mc^2\).

This equation informs why accelerating a spaceship to near-light speeds requires so much energy. As speed increases, time dilation and length contraction effects come into play, affecting both the spaceship and its travel through space.

Understanding this theory is crucial for grasping the demands of relativistic travel. It tells us:

• Mass appears to increase as velocity increases.
• Energy needed for further acceleration subsequently skyrockets.
• Objects cannot surpass the speed of light as per current physics laws.

Relativity guides predictions and plans for potential future interstellar missions.

Relativistic Mass

When we talk about relativistic mass, we mean that an object's mass appears to increase as its speed approaches the speed of light. This concept is central to Einstein's relativity, impacting high-velocity space travel.

As a spaceship picks up speed, especially approaching light speed, its mass isn't what we measure on Earth. Instead, it's "relativistic mass," a measure that incorporates the Lorentz factor: \(\gamma = \frac{1}{\sqrt{1-\left(\frac{v^2}{c^2}\right)}}\). As velocity \(v\) nears \(c\), the speed of light, \(\gamma\) increases, causing relativistic effects to dominate.

This means:

• Greater energy is necessary for acceleration as speed increases.
• This makes faster-than-light travel impossible with present technology.
• Rocket designs must accommodate ever-increasing energy needs as velocities rise.

Relativistic mass showcases the enormity of the task in mind for engineers aiming to explore beyond our solar system.

Speed of Light Travel

Traveling at the speed of light is a concept filled with wonder and enveloped in theory. According to relativity, reaching this speed is currently deemed impossible for any object with mass.

Why is exceeding this threshold unattainable? As an object accelerates towards light speed, its relativistic mass increases indefinitely, necessitating infinite energy to achieve even a hair's breadth closer to \(c\).

Several insights about light-speed travel include:

• Time stops for a traveler moving at light speed.
• To achieve this would require advancements in energy forms beyond nuclear fusion.
• Practical solutions might look at fractional \(c\) travel, such as 0.1 or 0.2 \(c\), significantly improving travel times without the prohibitive energy demands of full light-speed.

While theories of hypothetical particles like tachyons exist, in practical terms, our present understanding prevents any travel at or beyond light speed. These challenges fuel scientific speculation and drive research into future propulsion methodologies.