Question

Star $A$ is farther than star $B$ from the Earth. Which star will have a large parallax angle?

Answer 1

Hint:- Generally, the greater for the object which is close than the object is far away. By using this logic, whether the star $A$ has a large parallax angle or the star $B$ have a large parallax angle. Then, the solution can be determined.

Complete step by step solution:
Parallax angle is the angle between the two objects in space. For example, parallax angle is the angle between the earth and the star. The parallax angle is also used to find the distance between the star and the earth. Parallax formula states that the distance between the earth and the star is equal to the one divided by the parallax angle, where the parallax angle is measured in terms of the arc second. In the parallax angle, the nearby object shows a larger parallax angle than the far object.

Astronomers use an effect called parallax to measure distances to nearby stars. Parallax is the apparent displacement of an object because of a change in the observer's point of view. The parallax angle is changed when the observer is from a different position. This effect can be used to measure the distances to nearby stars. As the Earth orbits the Sun, a nearby star will appear to move against the more distant background stars. Astronomers can measure a star's position once, and then again 6 months later and calculate the apparent change in position. The star's apparent motion is called stellar parallax. The simple relation between the distance and the parallax angle is $d = \dfrac{1}{p}$, where, $d$ is the distance measured in parsecs and $p$ is the parallax angle.

Hence, the closer star $A$ will have the large parallax angle.

Note: Parallax angles of less than $0.01$ arcsec are very difficult to measure from Earth because of the effects of the Earth's atmosphere. This limits Earth based telescopes to measuring the distances to stars about $\dfrac{1}{{0.01}}$ or $100$ parsecs away.