A star is 5.89 light years from earth. calculate it's distance in parsec. how much parallax would this star show when viewed from two location of the earth six minths apart in its orbit around the sun?
Answers
Answer:
The distance of the star is,=4.29 ly
We know that one light year is the distance travelled by light in one year.
1 light year = 3×10
8
×365×24×60×60
=94608×10
11
m
Therefore, the distance in 4.29 ly can be written as:
4.29 ly=405868.32×10
11
m
We know that 1 Parsec is also the unit of distance and its value is:
1 parsec=3.08×10
16
m
Now, to express the distance in terms of parsec.
4.29ly=
3.08×10
16
405868.32×10
11
=1.32 parsec
The diameter of the Earth's orbit is,
d=3×10
11
m
The angle made by the star on the Earth's orbit can be given by:
θ=
405868.32×10
11
3×10
11
=7.39×10
−6
rad
But, the angle covered in 1sec=4.85×10
−6
rad
So, the parallax in viwing the star at two different positions of the Eart's orbit:
for, 7.39×10
−6
rad=
4.85×10
−6
7.39×10
−6
=1.52"