Problem 31 - Chemistry The Science in Context

Question

How long does it take moonlight to reach Earth when the distance to the moon is \(384,000 \mathrm{km} ?\)

Step-by-Step Solution

Answer

Answer: Approximately 1.28 seconds.

Step 1: Convert the distance in meters

The given distance between the Moon and the Earth is in kilometers, but we need to convert it to meters to match the units of the speed of light. We will use the conversion factor 1 km = 1000 m to do this conversion. \(d = 384,000 \mathrm{km} \times 1000 \mathrm{m/km} = 384,000,000 \mathrm{m}\)

Step 2: Use the formula to find the time taken

Now we will plug the values of distance and speed of light "c" into the formula \(t = \frac{d}{v}\). \(t = \frac{384,000,000 \mathrm{m}}{3.0\times10^8 \mathrm{m/s}}\)

Step 3: Compute the time

Divide the distance by the speed of light to get the time taken: \(t = \frac{384,000,000}{3.0\times10^8} = 1.28 \mathrm{s}\)

Step 4: Write the final answer

The time taken for the moonlight to reach Earth when the distance to the Moon is \(384,000 \mathrm{km}\) is approximately \(1.28 \mathrm{s}\).

Key Concepts

Speed of Light

The speed of light is one of the fundamental constants of nature. It is incredibly fast, clocking in at approximately \(3.0 \times 10^8\) meters per second (\(\text{m/s}\)). This speed means that light can travel across vast distances in a very short time. Because it is a constant, it is used frequently in calculations involving distances in space.

• Light speed constant: \(3.0 \times 10^8\) \(\text{m/s}\)
• Used to calculate how quickly light travels from one place to another
• Essential for understanding astronomical distances

Understanding the speed of light helps us make sense of the distances between celestial bodies, like how long it takes for moonlight to reach Earth.

Distance Conversion

Converting distances to the right units is key when performing calculations. In many physics problems, like the one discussed, you'll start with kilometers but need to move to meters since the speed of light is given in meters per second. Knowing how to convert is essential.

• 1 kilometer (km) = 1000 meters (m)
• Multiply the distance in kilometers by 1000 to convert to meters
• Ensures uniform units for accurate calculations

In our example, we converted the distance from the Moon to Earth from \(384,000\) km to \(384,000,000\) meters.

Moonlight

Moonlight is the reflection of sunlight off the surface of the Moon. When we talk about moonlight reaching Earth, we're measuring how long it takes for this reflected light to travel from the Moon to us. Since the distance from the Moon to Earth is approximately \(384,000\) kilometers, we can calculate the time taken using the speed of light.

• Moonlight is reflected sunlight
• The average Moon-Earth distance is \(384,000\) km
• Takes about 1.28 seconds for moonlight to reach Earth

This calculation is straightforward because of the uniform speed at which light travels, allowing us to easily determine the time it takes for moonlight to traverse the distance between the Moon and Earth.