Question

What is the parallax formula and how is it used to calculate the distance between two stars?

Answer 1

Parallax formula:

1. Astronomers use a phenomenon known as parallax to calculate distances to nearby stars.
2. The apparent displacement of an object caused by a change in the observer's point of view is referred to as parallax.
3. The method is based on measuring two angles and the included side of the star's triangle.
4. The following is the relationship between a star's distance and its parallax angle:

$\mathrm{d}=\frac{1}{\mathrm{p}}$

Here, $\mathrm{d}$ is the distance and $\mathrm{p}$ is parallax angle in radians.

Calculation of the distance between two stars:

1. In astronomy, the distances to other stars are too great to measure using the objects on the Earth's surface. Lucky for us, the Earth itself moves.
2. If we made two observations of the same star on opposite sides of the Earth's orbit, we would have a separation of 2 astronomical units or AU. One AU is the average distance from the Sun to the Earth. This is enough to get a noticeable angle α, between the star's two apparent locations. in the image ab, we can see that by cutting $\alpha$ in half, we get a right triangle where one leg is the distance between the sun and the other star. Let'slet $\frac{1}{2\alpha }=p$. We can to find the distance to that star. So $\tan p=\frac{1AU}{d}$.
3. Because the star will be very far away, we can assume that $\tan p$ is approximately equal to $p$. That reduces our parallax formula to $p=\frac{1AU}{d}$, or, in other words, $d=\frac{1AU}{p}$.