Question

The distance from the sun to Earth is \(1.496 \times 10^{8} \mathrm{~km}\). How long does it take light to travel from the sun to Earth?

Short answer

The time it takes light to travel from the sun to Earth is approximately 500 seconds or 8 minutes and 20 seconds.

Step-by-step solution

Determine Speed of Light

The speed of light in a vacuum is a constant, which is approximately 299,792 kilometers per second (km/s). This will be used as the velocity in the problem.

Calculate Time

Use the formula for time, which is distance divided by speed: time = distance/speed. Plug in the given distance from the sun to Earth and the speed of light to find the time it takes for light to travel.

Perform the Calculation

Using the distance of 1.496 x 10^8 kilometers and the speed of light, 299,792 km/s, calculate the time: 1.496 x 10^8 km / 299,792 km/s.

Convert to Appropriate Units

The calculated time will be in seconds. If needed, convert this to other units of time such as minutes or hours.

Key concepts

Distance from the Sun to Earth

Understanding the distance between the Sun and the Earth is fundamental in many areas of science, including astronomy and physics. An astronomical unit (AU) is the average distance from the Earth to the Sun, which is approximately \(1.496 \times 10^{8}\) km. Using this standardized measure helps scientists to communicate vast space distances in a more comprehendible way.

When we speak of light traveling from the Sun to the Earth, it's important to visualize this distance as not just vast, but consistently so. Scientific notation is invaluable here, as it provides a way to express such large numbers in a compact form. For example, stating that the Earth is \(1.496 \times 10^{11}\) meters away from the Sun quickly relays the magnitude without a train of zeroes.

Time Calculation in Physics

Timing how long it takes for light to reach from the Sun to the Earth involves applying a basic principle in physics: time is equal to the distance traveled divided by the speed of travel. The formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \) allows us to calculate the time it takes for light to cover the distance of one AU. This not only reinforces the concept of the speed of light being a universal constant but also underlines the importance of using consistent units when performing calculations.

To ensure accuracy, during the calculation it's crucial to ensure that the units for distance and speed are compatible—meters with meters per second (m/s) or kilometers with kilometers per second (km/s), for example. The solution to the exercise shows that by dividing the distance in kilometers by the speed of light also in kilometers per second, we obtain time directly in seconds.

Scientific Notation in Chemistry

Scientific notation is used across sciences, including chemistry, to represent very large or very small numbers. It's especially useful when dealing with the vast range of values encountered, from the size of atoms to the amount of atoms in a sample. A number is expressed in scientific notation by altering it into a product of a number (usually between 1 and 10) and a power of 10.

For instance, the number \(0.00000123\) would be written as \(1.23 \times 10^{-6}\). This makes complex calculations and comparisons more manageable, as it reduces the likelihood of error from miscounting zeros in standard form. It's a universally accepted and practical approach for dealing with both macroscopic and microscopic measurements. When applying scientific notation to our problem's solution, we find that it allows us to succinctly represent the immense distance between the Sun and Earth, facilitating clear and accessible calculations and communication.