·The light-year (ly) is a unit of distance commonly used in astronomy. It is defined as the dist

step 1 Alright, this question is all about light years. So light year, despite the name, is a unit of d

·The light-year (ly) is a unit of distance commonly used in...

Key Concepts

Light-Year

A light-year is a unit of distance that represents the distance light travels in a vacuum over the period of one year. It is a fundamental concept in astronomy used to express vast distances between celestial objects, providing a scale that is more intuitive than kilometers or miles for interstellar measurements.

Speed of Light

The speed of light in a vacuum is a fundamental constant in physics that defines the maximum speed at which all energy, matter, and information in the universe can travel. It is crucial for calculations in both theoretical and applied physics, serving as the basis for deriving distances like the light-year and for converting between different expressions of velocity.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another, ensuring that calculations remain consistent and accurate across different measurement systems. This concept is particularly important in physics and astronomy, where expressing measurements such as distance and speed in various units (e.g., kilometers, feet, years, nanoseconds) facilitates comparison and comprehension in different contexts.

Transcript

00:01 Alright, this question is all about light years.

00:05 So light year, despite the name, is a unit of distance.

00:11 It's not a unit of time.

00:16 But you might realize that distance is just equal to speed multiplied by time.

00:29 For example, if i get in my car and i drive at 60, my own, per hour, which is a speed, and i do that for two hours, i will have traveled 120 miles, my distance.

00:46 So similarly, we can figure out how long a light year is by figuring out the speed of light, which we already know, that's c times the time, which is one year.

01:04 Okay? so this is what we have to do to figure out how much much distance is in a light year.

01:11 All right, so we know that c is three times 10 to the eighth meters per second.

01:25 All right, and that's equal to that quantity, multiplied by 60 seconds per minute, multiplied by 60 seconds per minute, multiplied by 60 minutes, minutes per hour, this is just dimensional analysis, multiplied by 24 hours per day, multiplied by 365 days in one year.

02:08 Okay? so if we multiply all of this out, it's 3 times 60 times 60 times 24 times 365 times 365.

02:17 65 times 10 to the 8th.

02:23 This is the speed of light is 3 times 10 to the 8th meters per second.

02:28 That's true.

02:30 But it's also 9 .46 times 10 to the 15 meters per year.

02:43 Okay? now if i want to know what the distance in a light year is in kilometers, i need to figure out that one light year is equal to c in meters per year, multiplied by one kilometer, has 1 ,000 meters multiplied by my time, which is one year.

03:22 Okay, so i'm going to figure out that the meters are going to cancel out with the meters.

03:26 And the years are going to cancel out with the years.

03:29 I'm going to know that a light year is equal to c in meters per year divided by 1 ,000.

03:39 So it's going to be 9 .46 times 10 to the 15 minus 3.

03:49 That's 10 to the 15th over 10 to the 3rd times 10 to the 12 kilometers.

03:55 And that's how many kilometers are in one light year.

04:08 Okay? and then next part of the question is what is the speed of light in units of light year per year? this is kind of a trick question in a way.

04:25 So what is the speed of light? well, the speed of light is the distance over the time.

04:43 Okay? so this is the speed of light.

04:48 However, we want to express it.

04:51 Okay.

04:52 So our distance, well, we already know that one light year is the distance that light travels in a year.

05:03 So this is our distance.

05:04 And our time is one year...