the distance of alpha century from sun is 4.3 light years express the distance in parsec
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11th
Physics
Units and Measurement
Measurement of Length
The nearest star to our sol...
PHYSICS
The nearest star to our solar system is 4.29 light years away. How much is this distance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?
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ANSWER
Given:
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
1.52 Is correct Answer