FUTURE: consider changing wording of problem 1 to force students to do computations first
using matching units and radians and then (separately) doing it in arcsec/AU/pc system [DON’T
FORGET TO SHOW HOW TO DO THAT!!!!]
Also, be explicit that they should express results in arcsec ??!!!!!!!
Astronomy 321
Homework 3 --- Angles and Distances
Fall 2007
1. Binary star systems viewed from Earth
(i) Suppose there were a binary star at a distance of 1 pc from Earth and oriented perpendicular to the line of
sight from Earth. If this binary had a separation of 1 A.U., what would the angular separation in
arcseconds be, as viewed from Earth? What if it had a separation of 2 A.U.? 10 A.U.?
(ii) Suppose there were a binary star with a separation of 1 A.U. whose orientation was again perpendicular
to the line of sight from Earth. If the binary were at a distance of 1 pc, what would the angular
separation in arcsec be, as viewed from Earth? Repeat for distances of 2 pc and 10 pc and comment.
(iii). The star in Ursa Major known as Mizar is a binary star. The angular separation between the two stars
is 14.5 arcsec, and the system is about 27 pc away. What is the (minimum) physical separation
between the two stars, in A.U.?
2. Estimating the distance to a nearby galaxy
The Andromeda galaxy subtends about 3 degrees on the sky. Suppose Andromeda has about the same
diameter as the Milky Way (about 100,000 ly). What would the distance to Andromeda be in ly and in pc?
Look up the distance to Andromeda on the web or in a textbook. Did the simple estimate give the right
order of magnitude?
3. Angular sizes of the stars
Suppose the Sun (a fairly typical star) were 10 pc away (the distance to some of the closest stars). What
would its angular size (angular diameter) be in arcseconds? The Sun's radius is about 700,000 km.
4. Calibrate your hand for angular measures
(i) Suppose we want to draw two lines on the board that will be 1 degree apart, as viewed from a
distance of 10 meters. How far apart should the two lines be drawn (to nearest mm)?
(ii) Repeat for angles of 3, 5, and 10 degrees
(iii) Repeat for angles of 1 arcminute and 1 arcsecond.
5. Radians and skinny triangles
We said in class that for "sufficiently small" angles, sin()  , where the angle is measured in radians.
Experiment with different numbers on your calculator to find the largest angle for which this equality is
accurate to 2 significant digits. Express your result in radians first and then in degrees.