Question

The parallax method of measuring star distances gives most accurate results when the gap between two observations of a star is about six months. Which of these statements best explains why a gap between observations affects the accuracy of the star distance?
a. It allows the star to complete its life cycle and evolve from one form to another.
b. It ensures that measurements are taken from two points which are very far apart.
c. It makes up for the changes in the star's position due to its movement around the sun.
d. It helps to take the measurement of changes in the position of the star due to supernova explosions.

Answer 1

b. It ensures that measurements are taken from two points
that are very far apart.

Measurements taken six months apart are the farthest apart
that an astronomer can ever get ... they're on opposite sides
of the Earth's orbit !

Answer 2

Answer:

b). It ensures that measurements are taken from two points which are very far apart.

Explanation:

In parallax method of measurement of the distance of far or distant objects we know that we use the method of distance geometry

It is given as

$angle = \frac{arc}{radius}$

now we have

Arc = distance between two positions from which angle is measured

Angle = total angle subtends by the planet at two positions

radius = distance of the planet

so we will have

$distance = \frac{arc}{angle}$

so here if we ensure large arc length then the error in the measurement of the angle will be small and the distance will be accurate.