An astronaut travels to a star system 4.5 ly away at a speed of 0.90c. Assume that the time needed to accelerate and decelerate is negligible. How long does the journey take according to Mission Control on earth?

검증된 단계별 안내

Step 1: Identify the given values in the problem. The distance to the star system is 4.5 light-years (ly), and the speed of the astronaut is 0.90c, where c is the speed of light (approximately 3.00 × 10⁸ m/s).

Step 2: Recall the formula for time, which is derived from the relationship between distance, speed, and time:

t = \frac{d}{v}

, where

t

is the time,

d

is the distance, and

v

is the velocity.

Step 3: Substitute the given values into the formula. The distance

d

is 4.5 ly, and the velocity

v

is 0.90c. The formula becomes:

t = \frac{4.5}{0.90}

(in light-years per year).

Step 4: Simplify the fraction to determine the time

t

in years. Note that the units of light-years and years are consistent, so no unit conversion is necessary.

Step 5: Conclude that the time calculated represents the duration of the journey as observed by Mission Control on Earth, since the calculation is based on the distance and speed in the Earth reference frame.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Light-Year (ly)

A light-year is a unit of distance that represents how far light travels in one year. Since light moves at approximately 299,792 kilometers per second, one light-year is about 9.46 trillion kilometers. This concept is crucial for understanding astronomical distances and helps quantify the vastness of space, such as the 4.5 light-years to the star system in the question.

Relativistic Speed

Relativistic speed refers to velocities that are a significant fraction of the speed of light (denoted as 'c'). At these speeds, the effects of Einstein's theory of relativity become significant, particularly time dilation and length contraction. In this scenario, the astronaut's speed of 0.90c means that relativistic effects must be considered when calculating the journey's duration from different reference frames.

Time Dilation

Time dilation is a phenomenon predicted by Einstein's theory of relativity, where time passes at different rates for observers in different frames of reference. For an observer moving at a relativistic speed, time appears to pass more slowly compared to an observer at rest. This concept is essential for understanding how the journey duration is perceived by Mission Control on Earth versus the astronaut traveling at 0.90c.