Question

Astronomy How long does it take a beam of light to reach Earth from the Sun when the Sun is 93,000,000 miles from Earth? Express your answer in seconds, using scientific notation.

Short answer

Time ≈ 500 seconds or 5.0 × 10^2 seconds.

Step-by-step solution

Identify Given Values

The distance from the Sun to the Earth is 93,000,000 miles. The speed of light is approximately 186,282 miles per second.

Set Up the Formula

The time it takes for light to travel a certain distance can be found using the formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \] Here, the distance is 93,000,000 miles and the speed of light is 186,282 miles per second.

Calculate the Time

Substitute the given values into the formula: \[ \text{time} = \frac{93,000,000 \text{ miles}}{186,282 \text{ miles/second}} \] Perform the division to get the time.

Converting to Scientific Notation

After calculating, approximate the result and express it in scientific notation.

Key concepts

distance and speed relationship

Let's start by understanding the relationship between distance and speed. When you want to find out how long it takes for something to travel a certain distance, you use the basic formula: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \] This formula tells us that time is equal to the distance traveled divided by the speed. The faster you move, the less time it will take to cover the same distance.
For example, if you walk 10 miles at 5 miles per hour, it will take you 2 hours.
This concept is essential for our problem because we need to know how long light takes to travel from the Sun to the Earth. Once we know the distance (93,000,000 miles) and the speed of light (186,282 miles per second), we can use our formula to find the time.

scientific notation

Next, let's dive into scientific notation. Scientific notation is a way to express really large or really small numbers more conveniently. It makes calculations easier and helps save space. Instead of writing out all the zeros in 93,000,000, for example, we can write it as \( \text{9.3} \times 10^7 \).
This breaks the number into two parts:

• The significant figures (in this case, 9.3).
• The power of 10 (showing how many places we move the decimal point).

This method isn't just for large numbers. Very small numbers, like the size of bacteria, can also be written in scientific notation. For example, 0.000001 could be written as \( \text{1} \times 10^{-6} \). In our problem, after we find the time it takes for light to travel from the Sun to the Earth, we'll express that time in scientific notation for simplicity and accuracy.

speed of light

Finally, let's talk about the speed of light. Light is incredibly fast. It travels at \( 186,282 \text{ miles per second}\).This means that in one second, light can travel about 186,282 miles. That's almost 7.5 times around Earth in just one second! Understanding the speed of light is important because it allows us to calculate how long it takes light to travel across different distances.
Imagine you turn on a flashlight and point it towards a wall. The light reaches the wall almost instantly because the distance is very short. However, light from the Sun takes about 8 minutes to reach us, despite being very fast, because the distance (93 million miles) is incredibly large. This understanding helps us figure out the light travel time in various scenarios, including our solar system and beyond.