Question

We would be more likely to get an accurate measurement of the distance from Earth to a nearby star if we took the angular measurements at times separated by what time interval?

Answer 1

Answer:

6 month interval

Explanation:

The distance to a nearby star in theory is more simple than

one might think! First we must learn about the parallax effect. This is the mechanism our eyes use to perceive things at a distance! When we look at the star from the earth we see it at different angles throughout the earth's movement around the sun similar to how we see when we cover on eye at a time. Modern telescopes and technology can help calculate the angle of the star to the earth with just two measurements (attached photo!) Since we know the distance of the earth from the sun we can use a simple trigonometric function to calculate the distance to the star. The two measurements needed to calculate the angle of the star to the earth caused by parallax (in short angle θ) are shown in the second attached photo.

So using a simple trigonometric function $Sin\theta=\frac{r}{d}$ we can solve for d which is the distance of the earth to the star:

$d=\frac{r}{Sin\theta}$

In the first attached photo a picture where r is the distance to the star and the base of the triangle is the diameter of the earth.