Problem 18 - Applied Physics

Question

Light from the sun travels \(1.50 \times 10^{8} \mathrm{~km}\) to reach the earth. How long does its journey take in minutes?

Step-by-Step Solution

Answer

The light takes about 8.33 minutes to reach Earth.

Step 1: Understand the Problem

We need to find out how long it takes for light to travel from the sun to the earth. We know the distance is \(1.50 \times 10^8\) km, and we need to determine the time it takes in minutes.

Step 2: Speed of Light

Recall that the speed of light in a vacuum is approximately \(3.00 \times 10^5\) km/s. We'll use this speed to calculate the time taken for light to travel the given distance.

Step 3: Calculate Time in Seconds

Using the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\), we calculate the time it takes in seconds: \[\text{Time (s)} = \frac{1.50 \times 10^8 \text{ km}}{3.00 \times 10^5 \text{ km/s}}.\] This evaluates to approximately \(500\) seconds.

Step 4: Convert Seconds to Minutes

Since there are 60 seconds in a minute, convert the time from seconds to minutes by dividing by 60: \[\text{Time (min)} = \frac{500 \text{ s}}{60 \text{ s/min}}.\] This gives approximately \(8.33\) minutes.

Key Concepts

Distance and Time Calculation

When we calculate how long it takes for something to travel a certain distance, we use the formula, \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \). This formula tells us that time is the result of dividing the distance by the speed at which something is moving.
Light travels incredibly fast, and we often measure its speed in kilometers per second.
So, when we want to know how long it takes light to travel a given distance, we simply use the known values of distance and speed in our formula.

• The distance light travels from the sun to the Earth is \(1.50 \times 10^8 \) km.
• The speed of light is \(3.00 \times 10^5 \) km/s.

By inserting these values into the formula, we can calculate the exact time it takes for light to cover the journey. This is a fundamental principle for understanding how to calculate time when speed and distance are known.

Solar System Distances

The solar system is vast, and understanding the distances within it is key to grasping how long it takes for anything to travel through space.
For example, the distance from the Earth to the Sun, also known as an Astronomical Unit (AU), is \(1.50 \times 10^8 \) kilometers.
This scale gives us a sense of the immense spaces between celestial objects.

• Understanding these distances helps us to calculate travel times for light and other astronomical phenomena.
• These distances also highlight how vast our solar system truly is, providing perspective on the time scales involved in space travel.

By familiarizing ourselves with these distances, we gain a better understanding of the measurements and conversions astronomers use regularly. This helps bridge the gap between conceptualizing light travel and the distances it must traverse.

Light Travel Time

Light travels at an almost unimaginably fast speed of \(3.00 \times 10^5 \) km/s. This speed allows light to cover enormous distances in space in a relatively short amount of time.
When we speak about light travel time, we are referring to how long it takes for light to move from one point to another.
To calculate how long it will take light to travel, we divide the distance by the speed to get the time. For a journey from the Sun to Earth, it takes approximately 8.33 minutes, as the calculations show:

• Travel time is the key components in understanding how we observe distant stars and galaxies, as light must travel from these objects to reach us.
• Remembering the quick travel time helps puts into perspective how vast the distances still are despite light's speed.

Developing an intuition for light travel time aids in appreciating the incredible nature of the universe and the speed with which light bridges vast spaces.