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Answer:
a) How many parsecs are there in one astronomical unit?
(b) How many meters are in a parsec?
(c) How many meters in a light-year?
(d) How many astronomical units in a light-year?
(e) How many light-years in a parsec?
3.26ly
Explanation:
The parallax angle can be used to find out the distance using triangulation. Making a triangle between the nearby star, the Sun and the Earth, knowing that the distance between the Earth and the Sun () is defined as 1 astronomical unit:
Where d is the distance to the star.
Since p is small it can be represent as:
(1)
Where p(rad) is the value of in radians
However, it is better to express small angles in arcseconds
(2)
Then, equation 2 can be replace in equation 1:
(3)
From equation 3 it can be see that
<em>a) How many parsecs are there in one astronomical unit? </em>
⇒
<em>(b) How many meters are in a parsec? </em>
⇒
<em>(c) How many meters in a light-year? </em>
To determine the number of meters in a light-year it is necessary to use the next equation:
Where c is the speed of light () and x is the distance that light travels in 1 year.
In 1 year they are 31536000 seconds
<em>(d) How many astronomical units in a light-year?</em>
⇒
<em>(e) How many light-years in a parsec?</em>
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