Distances, Angles and Parallax

Question 1

What can we approximate if angles are small?

Answer 1

sin(x) = x = tan(x)

x is in radians

Question 2

What is the equation for the angular size of an object?

Answer 2

α = L/d

Question 3

What is trigonometric parallax?

Answer 3

Finding the distance to a star by measuring the amount it shifts in the sky every half period of orbit around the Sun.

Question 4

What is the Earth-Sun distance?

Answer 4

1AU ~ 150 million km

Question 5

What is the equation for the parallax angle if it is small?

Answer 5

p = 1AU/d

Question 6

What is 1 parsec?

Answer 6

The distance at which a star makes a parallax angle of 1 arc second.

Question 7

What is the equation for the distance to a star in parsecs?

Answer 7

d(pc) = 1/parallax angle (rad)

Question 8

What are reference stars?

Answer 8

Relative angle measurement made in comparison to more distant reference stars.

Question 9

How do you work out the value of 1 parsec?

Answer 9

1AU/(1/3600 * 2pi/360)

Question 10

How do you work out angles using arc minutes and arc seconds?

Answer 10

Convert them into degrees and add them all together.

Question 11

What do you need before you can measure the parallax?

Answer 11

The proper motion of a star (the amount it drifts across the sky).