Question

If an astronomical object's parallax is one-half arcsecond, how many parsecs is it from Earth?

Answer 1

thw answer is C. 2

i do not know why! Sorry!

i just took the test and it was right

Answer 2

Answer:

C. 2

Explanation:

The angle due to the change in position of a nearby object against the background stars is known as parallax (see the image below).

The parallax angle can be used to find out the distance by means of triangulation (as is shown in the image below), knowing that the distance between the Earth and the Sun (150000000 Km) is defined as 1 astronomical unit (AU):

$\tan{p} = \frac{1AU}{d}$

Where d is the distance to the star.

$p('') = \frac{1}{d}$    (1)  

Equation (1) can be rewritten in terms of d:

$d(pc) = \frac{1}{p('')}$  (2)

Equation (2) represents the distance in a unit known as parsec (pc).

The astronomical object with a parallax of one-half arcsecond ($p('') = \frac{1}{2}$) will be replace in equation 2:

       

$d(pc) = \frac{1}{(\frac{1}{2})}$

$d(pc) = 2$

Hence, the object is 2 parsecs away from Earth.