Respuesta :
Answer:
[tex]\\2.647191386*10^{20}m[/tex]
Explanation:
To answer this question it is necessary to understand that Light travels in vacuum at a constant speed, which means an important property to estimate distances in Universe. We already know that speed of light in vacuum is exactly 299,792,458 m/s.
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 the distance that light travels in one year, 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 meters.
How many seconds are there in a year?
[tex]\\ 1year = 365 days * \frac{24h}{day}*\frac{60min}{h}*\frac{60s}{min}=31,536,000s[/tex].
That is, there are 31,536,000 seconds in a year.
What is the distance that light travels in one year?
Because light travels at a constant speed, the distance can be calculated as follows:
[tex]\\ Speed = \frac{distance}{time}[/tex]
or, equivalently,
[tex]\\ distance = Speed * time[/tex]
So,
[tex]\\ distance = 299792458\frac{m}{s} * 31536000s [/tex]
But, we can see that these are big numbers, and a better way to deal with this is to use scientific notation or floating-point numbers.
Then,
[tex]\\ 299792458\frac{m}{s} = 2.99792458 * 10^{8}\frac{m}{s}[/tex]
and,
[tex]\\ 31536000s = 3.1536000*10^{7}s[/tex]
So,
[tex]\\ 2.99792458 * 3.1536000 = 9.45425495 [/tex], and,
[tex]\\ 10^{8}*10^{7} = 10^{8 + 7} = 10^{15}[/tex]
Then, the total distance that light travels in a year is:
[tex]\\ 9.45425495 * 10^{15}m[/tex]
But we now that The Sun is 28,000 light-year from the center of the Milky Way galaxy, and that 28000light-year= [tex]\\2.8 *10^{4}[/tex] light-year.
So, the distance in meters of The Sun from the center of the Milky Way galaxy is:
[tex]\\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[/tex]
Then, the answer is:
[tex]\\2.647191386*10^{20}m[/tex].
Likewise, the answer could be found as a matter of proportions, mostly because light travels the same distance at each time:
If light travels [tex]\\ 9.45425495 * 10^{15}m[/tex] in a light-year, how many meters does light travel in 28,000 light-year?
[tex]\frac{9.45425495* 10^{15}m}{light-year}[/tex] = [tex]\frac{X meters}{2.8*10^{4}light -year}[/tex]. or
[tex]\\ X =\frac{9.45425495* 10^{15}m}{light-year} * {2.8*10^{4}light -year}=2.647191386*10^{20}m[/tex]
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.
