Quiz 2

Problems 2.1

Description: Tycho Brahe's observations of the stars and planets were accurate to about 1 arc minute (1′). (a) To what distance does this angle correspond at the distance of the Moon?

This is how I understand the problem:

They are asking for the distance between points A and B. The angle between the observer and those two points is 1 arc minute, this is also called angular distance.

To solve the problem:

We can think of the distance between points A and B as a little piece of a big circle

A circle is 360 degrees and the radius is the distance to the Moon

distance between A and B = angular distance x circumference / 360 degrees

The circumference is 2 x pi x r, where r is the distance to the Moon (3.844 x 10^5 km). The angular distance is 1 arc min, and there are 60 arc minutes in 1 degree. Since we want the angular units to cancel we have to convert arc minutes to degrees or degrees to arc minutes.

To convert arc minutes to degree => 1 arc min x 1 degree / 60 arc min = 0.0167 degree

distance between A and B = 0.0167 degrees x 2 x pi x 3.844 x 10^5 km/360 degrees = 111.82 km

For parts (b) and (c), the same applies. You are only going to be using a different radius for the circle. The larger the radius, the larger the distance between points A and B.