Question

correctly conclude? The star Wolf 1061 has a parallax of 2.34 arc seconds, while the star Ross 652 has a parallax of 1.70 arc seconds. What can you correctly conclude?

Answer 1

Answer:

It can be concluded that the star Ross 652 is farther away from Earth than the star Wolf 1061.

Explanation:

The angle due to the change in position of a nearby object against the background stars it is known as parallax. This angle is gotten when the position of the object is measured in January and then in July according with the configuration of the Earth with respect to the Sun in those months (see the image below).

The parallax angle can be used to find out the distance by means of triangulation. Making a triangle between the nearby star, the Sun and the Earth(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:

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

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), that is the distance of a star with a parallax angle of 1 arc second.

-The case for star Wolf 1061, $p('') = 2.34 arc seconds$:

$d(pc) = \frac{1}{2.34}$

$d(pc) = \frac{1}{2.34}$

$d(pc) = 0.42 pc$

But $1pc = 3.09x10^{13} Km$, therefore:

$0.42pc . \frac{3.09x10^{13} Km}{1pc}$ ⇒ $1.2978x10^{13} Km$

Or it can be expressed in light years, since $1pc = 3.26 ly$:

$0.42pc . \frac{3.26 ly}{1pc}$ ⇒ $1.3692 ly$

In which 1 light year corresponds to the distance traveled for light in one year.

So the star Wolf 1061 is at a distance of $1.2978x10^{13} Km$.  

-The case for star Ross 652, $p('') = 1.70 arc seconds$:

Following the same approach above.

$d(pc) = \frac{1}{1.70}$

$d(pc) = \frac{1}{1.70}$

$d(pc) = 0.58 pc$

But $1pc = 3.09x10^{13} Km$, therefore:

$0.58pc . \frac{3.09x10^{13} Km}{1pc}$ ⇒ $1.7922x10^{13} Km$

Or it can be expressed in light years, since $1pc = 3.26 ly$:

$0.58pc . \frac{3.26 ly}{1pc}$ ⇒ $1.8908 ly$

So the star Ross 652 is at a distance of $1.7922x10^{13} Km$.

So it can be concluded that the star Ross 652 is farther away from Earth than the star Wolf 1061.