Homework 1. The Sun & You

Name: ________________________ DUE 9/04 ID number: ________________________

As you have seen in class, astronomers often compare things by taking ratios. For example, we might compare the mass of Jupiter to the mass of the Sun by dividing the Sun's mass by Jupiter's mass (and find that the Sun is about a thousand times more massive than Jupiter). In this assignment you will compare yourself to the Sun.

The Sun's diameter, mass, and age can all be found in the book, but for convenience the numbers you need are given here. Notice the little `' symbol after the diameter D, mass M, and age A; this is the astronomical symbol for the Sun, and indicates that these quantities refer to the Sun.

Diameter: D = 1.39 × 109 meters = 4.57 × 109 feet.
Mass: M = 1.99 × 1030 kg = 4.38 × 1030 lb.
Age: A = 4.5 × 109 years = 1.42 × 1017 seconds.

Now fill in your `diameter', mass, and age in the spaces below, where the small `y' symbol indicates that these quantities refer to you. To keep things simple, assume that your diameter is equal to your height, and your mass is equal to your weight; if you'd rather not reveal personal information, use make-believe numbers. Important: make sure to write down the units for your diameter, mass, and age!

Diameter: Dy = ________________________________
Mass: My = ________________________________
Age: Ay = ________________________________

Now divide the Sun's diameter, mass, and age by your diameter, mass, and age. Be sure to use the same units for both; for example, if you use the Sun's mass in kilograms, you should express your mass in kilograms also. This way, the units will cancel out when you divide, and the result will be a ratio with no units of any kind. This is important because a ratio does not depend on the units you started with - for example, you should get the same ratio of the Sun's mass to your mass whether you measure both in kilograms, pounds, tons, or ounces!

D ÷ Dy = __________________________________________________
M ÷ My = __________________________________________________
A ÷ Ay = __________________________________________________

So far, this has all been pretty straightforward, and if you know how to use scientific notation then you shouldn't have any serious problem. But now I'd like you to answer a few questions based on your results above:

1. In which way are you most like the Sun? That is, of the three properties you've compared - diameter, mass, and age - in which one are you and the Sun most similar?

2. In which way are you least like the Sun? That is, in which property are you and the Sun most different?

3. Are you surprised by your answers to the two questions above? Why or why not?

Finally, if all this makes you feel very small and insignificant in comparison to the mighty Sun, don't worry. We'll come back to this and discover that, in one very surprising way, human beings actually outclass the Sun.

Joshua E. Barnes (barnes@ifa.hawaii.edu)

Last modified: August 26, 2001