The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km, is Proxima Centauri from the sun?

Video transcript

Welcome back everyone to another video. The nearest star to our sun is Proxima Centauri at a distance of 4.3 light years from the sun. A light year is the distance that light travels in one year or 365 days. How far away in kilometers is Proxima Centauri from the sun? And we're given for answer choices. A 4.3 multiplied by 10 to the 15th. B 1.5 multiplied by 10 to the eighth. C 8.1 multiplied by 10 to the eighth and D 4.1 multiplied by 10 to the power of 13th. So let's solve this problem. And we can do this using two different ways. First of all, we can just understand that distance is equal to velocity multiplied by time if velocity is constant. So we can either use this formula or we can use the analysis. So first of all, what we're going to do is just introduce our given which is 4.3 light years and we can just use a shorthand notation LY. And what we want to understand is that this is our time. So this is our tea right. However, if we want to get kilometers as our distance, we want to convert those light years into days and finally seconds. The reason why we need seconds is because we know that the speed of light C is equal to 3.0 multiplied by 10 to 8 m per second. Ok. So that be our velocity and since it's given in seconds, our goal is to convert a light years into seconds. So let's do that. First of all, we know that one light here is equivalent to 365 days. So that's why we're using our first conversion factor. And we can clearly see that the light years cancel each other out. And we get this, our ultimate goal is to get seconds. That means we now want to get rid of the days and we need to think of a conversion factor. We know how many hours we have in one day, one day is equivalent to 24 hours. And now we cancel out the days. Currently, we have our time and our, and we just want to continue. Now, we want to go from ours to seconds. So we put hours on the bottom seconds on top, we know that one hour is equal to 3600 seconds. Ok. Now, we clearly see that so far we have seconds. That's our time. Exactly what we want to get for our units, right? Ok. So now what, well, we need an additional conversion factor. Eventually, our goal is to get kilometers. But first of all, we need to get meters because we are given our speed of light. So if we have seconds on top, we can put seconds on the bottom for the next conversion factor to cancel seconds out. And now we're going to use meters on top. Ok? Because that's the conversion factor that we have and we know that there are 3.0 multiplied by 10 to 8 m in one second. Based on the conversion factor coming from the speed of light, what we notice is that our seconds cancel each other out and we end up with meters. And finally, now that we have meters, we want to convert that into kilometers. Do we put meters on the bottom kilometers on top? And now how many meters do we have in one kilometer? Well, basically that's 10th of the third and we eventually see that we have arrived at kilometers, let's perform the calculations. And in this case, if we do the math, we see that the answer should be 4.1 multiplied by 10 to the power of 13 kilometers, which essentially corresponds to the answer. Choice D. That would be our final answer. And thank you for watching.