Question

In astronomy, distances are measured in light-years, the distance that light travels in one year. What is the distance of one light-year expressed in kilometers?

Short answer

A light-year is approximately \(9.461 \times 10^{12}\) kilometers.

Step-by-step solution

Determine the seconds in a year

There are \(60\) seconds in a minute, \(60\) minutes in an hour, \(24\) hours in a day, and \(365\) days in a year. So, the total number of seconds in a year can be calculated as follows: \(60 \times 60 \times 24 \times 365 = 31,536,000\) seconds.

Calculate the total kilometers light travels in one year

Using the formula for distance, \(Distance = Speed \times Time\), substitute the speed of light (\(299,792\) kilometers per second) and the time (number of seconds in a year) into the formula, \(Distance = 299,792 \times 31,536,000\).

Calculate the distance

Calculate the result of the multiplication in the previous step, which gives the distance of one light-year in kilometers.

Key concepts

Speed of Light

The speed of light is one of the fundamental constants in physics, critical for understanding astronomical measurements. Light travels at an astonishing speed of 299,792 kilometers per second in a vacuum. This speed is constant and unchanged, making it a reliable measure for long distances in the universe. Light’s speed allows us to calculate how far it travels in a given time. For example, in one second, light can traverse nearly 300,000 kilometers, which is roughly seven times the circumference of Earth!

• Speed of light in vacuum: 299,792 kilometers per second (or about 186,282 miles per second).
• The velocity of light remains constant and is not affected by the movement of the source or observer.

Understanding the speed of light enables astronomers to measure vast cosmic distances using units like light-years.

Astronomical Measurements

Astronomical measurements rely heavily on the concept of light-years to grasp the immense expanse of the universe. A light-year is the distance that light travels in one year, making it a unique method for measuring astronomical distances. While kilometers are suitable for measuring distances on Earth, the vastness of space requires a more practical unit to express the enormous separations between celestial objects.

• One light-year is equivalent to 9.461 trillion kilometers.
• Astronomers use light-years to express distances to stars, galaxies, and other astronomical objects.

Light-years help compare distances to faraway stars and galaxies, providing a graspable scale for human comprehension.

Unit Conversion

In astronomy, converting units is essential for interpreting and understanding data. Since many scientific measurements are taken in different units, converting these into a common metric, such as kilometers, is crucial. When calculating the distance of one light-year, we start by determining the number of seconds in a year, which is approximately 31,536,000 seconds.

To find the distance light travels in one year, use the formula:\[\text{Distance} = \text{Speed} \times \text{Time}\]Given the speed of light as 299,792 kilometers per second, multiply it by the number of seconds in a year:\[299,792 \times 31,536,000 = 9,461,000,000,000 \text{ kilometers}\]Converting time and speed into distance helps in understanding and interpreting astronomical data.

Physics of Light

The physics of light is a broad field, explaining phenomena related to light and its behavior. Light is a form of electromagnetic radiation, encompassing a spectrum from gamma rays to radio waves. Although invisible to the naked eye, these spectra are vital in understanding and exploring the universe.

Understanding light's properties involves recognizing its dual nature - both as waves and particles (photons). This behavior aids scientists in measuring distances and analyzing celestial bodies.

• Wavelength and frequency affect light's energy and color perception.
• Light interacts with mediums, demonstrating refraction and reflection.

Physics of light underpins many technologies, including telescopes and imaging devices, essential for astronomical studies.