Answer:
![\\2.647191386*10^{20}m](https://tex.z-dn.net/?f=%5C%5C2.647191386%2A10%5E%7B20%7Dm)
Explanation:
To answer this question it is necessary to understand that Light travels in vacuum at a <em>constant</em> speed, which means an important property to estimate distances in Universe. We already know that <em>speed of light in vacuum is exactly 299,792,458 m/s.</em>
To solve this question, we need to answer these two ones:
- What is the distance that light travels in one year?
- How many seconds are there in a year?
In the first question, we need to know <em>the distance that light travels in one year, </em>which give us some clue to respond the distance that light travels in 28,000 light-years.
The answer to the second question it is crucial to answer the first question in <em>meters</em>.
<h3>How many seconds are there in a year?</h3>
.
That is, there are 31,536,000 seconds in a year.
<h3>What is the distance that light travels in one year?</h3>
Because light travels at a constant speed, the distance can be calculated as follows:
or, equivalently,
![\\ distance = Speed * time](https://tex.z-dn.net/?f=%5C%5C%20distance%20%3D%20Speed%20%2A%20time)
So,
![\\ distance = 299792458\frac{m}{s} * 31536000s](https://tex.z-dn.net/?f=%5C%5C%20distance%20%3D%20299792458%5Cfrac%7Bm%7D%7Bs%7D%20%2A%2031536000s%20)
But, we can see that these are <em>big numbers</em>, and a better way to deal with this is to use scientific notation or <em>floating-point numbers</em>.
Then,
![\\ 299792458\frac{m}{s} = 2.99792458 * 10^{8}\frac{m}{s}](https://tex.z-dn.net/?f=%5C%5C%20299792458%5Cfrac%7Bm%7D%7Bs%7D%20%3D%202.99792458%20%2A%2010%5E%7B8%7D%5Cfrac%7Bm%7D%7Bs%7D)
and,
![\\ 31536000s = 3.1536000*10^{7}s](https://tex.z-dn.net/?f=%5C%5C%2031536000s%20%3D%203.1536000%2A10%5E%7B7%7Ds)
So,
, and,
Then, the <em>total distance that light travels in a year</em> is:
But we now that The Sun is <em>28,000 light-year</em> from the center of the Milky Way galaxy, and that 28000light-year=
light-year.
So, the distance in meters of The Sun from the center of the Milky Way galaxy is:
![\\9.45425495 * 10^{15}m * 2.8 *10^{4}light-year =26.47191386*10^{15}*10^{4}=26.47191386*10^{15+4}=26.47191386*10^{19}=2.647191386*10^{20}m](https://tex.z-dn.net/?f=%5C%5C9.45425495%20%2A%2010%5E%7B15%7Dm%20%2A%202.8%20%2A10%5E%7B4%7Dlight-year%20%3D26.47191386%2A10%5E%7B15%7D%2A10%5E%7B4%7D%3D26.47191386%2A10%5E%7B15%2B4%7D%3D26.47191386%2A10%5E%7B19%7D%3D2.647191386%2A10%5E%7B20%7Dm)
Then, the answer is:
.
Likewise, the answer could be found as a <em>matter of proportions</em>, mostly because light travels the same distance at each time:
If light travels
in a light-year, how many meters does light travel in 28,000 light-year?
=
. or
![\\ X =\frac{9.45425495* 10^{15}m}{light-year} * {2.8*10^{4}light -year}=2.647191386*10^{20}m](https://tex.z-dn.net/?f=%5C%5C%20X%20%3D%5Cfrac%7B9.45425495%2A%2010%5E%7B15%7Dm%7D%7Blight-year%7D%20%2A%20%7B2.8%2A10%5E%7B4%7Dlight%20-year%7D%3D2.647191386%2A10%5E%7B20%7Dm)
That is, the same result.
Notice that we calculate the result using 1 year = 365days. We can add more precision to our answer if we consider 1 year = 365,25days, following the same steps.
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