Question

Space Distances Find the distance in AUs to a star 68 light-years (LY) distant. ( \(1 \mathrm{LY}=6.3 \times\) \(10^{4} \mathrm{AUs}\) )

Short answer

The star is 4,284,000 AUs away.

Step-by-step solution

Understand the Given Values

We need to find the distance to a star in Astronomical Units (AUs) given it is 68 light-years away. We know from the problem that 1 light-year is equivalent to \(6.3 \times 10^4\) AUs.

Set Up the Conversion

The task is to convert 68 light-years into AUs. We can do this by multiplying the number of light-years by the number of AUs per light-year.

Perform the Calculation

Multiply the number of light-years (68) by the conversion factor for AUs per light-year, which is \(6.3 \times 10^4\) AUs.\[68 \times 6.3 \times 10^4 = 4284000 \text{ AUs}\]

State the Result

The distance from Earth to the star is 4,284,000 AUs.

Key concepts

Understanding Light-Years

When talking about vast distances in space, astronomers often use light-years. A light-year is the distance light travels in when it travels for a whole year. Since light moves extremely fast at approximately 299,792 kilometers per second, a single light-year equals around 9.46 trillion kilometers.
Light-years are preferable in astronomy because celestial distances are far too immense to conveniently express with kilometers or miles. A light-year is an effective way to express these distances on a more manageable scale.

• A light-year measures distance, not time.
• It helps describe the space between stars and galaxies.

This unit allows us to appreciate just how far light travels in the vacuum of space, opening up perspectives on how expansive and vast our universe is.

Conversion Between Distance Units

Converting distance units, like from light-years to astronomical units (AUs), is essential in astronomy. It helps us understand space in smaller, manageable measurements. One light-year is equivalent to approximately 63,000 astronomical units. The conversion enables astronomers to specify routes and distances more accurately for calculations.
To convert light-years into astronomical units, you can employ a straightforward mathematical formula:

• Use the conversion factor: 1 light-year = 63,000 AUs.
• Multiply the number of light-years by 63,000 to find the distance in AUs.
• For example, 68 light-years become: \( 68 \times 6.3 \times 10^4 \) AUs.

This results in 4,284,000 AUs, facilitating a better grasp of the distance for various astronomical observations and calculations.

Astronomy Education: Making Sense of Space

Educating oneself about the concepts of astronomical distances involves understanding how different units work and their practicality in describing the cosmos. Astronomy education seeks to demystify these, making them comprehensible and relatable to everyday experiences.
By highlighting tools like light-years and astronomical units, learners can:

• Visualize the enormity of space.
• Grasp the relationships between celestial bodies' distances.
• Appreciate the methods astronomers use for calculations across vast scopes.

Moreover, such education grows appreciation for technology that measures and conveys these distances, emphasizing astronomy's role in uniting scientific exploration and human curiosity about the universe.