The Sun & You: Discussion

Most people did pretty well. One error which several people made was to write 10¹ (= 10) when they should have put 10⁰ (= 1); for example,

1.75 × 10¹ m

= 17.5 m

= 57.4 ft

Alice as a giant in the White Rabbit's house

Another somewhat common error was to mix units, for example:

(4.5 × 10⁹ yr) ÷ (5.7 × 10⁸ sec) = 7.9 (yr/sec) = 7.9 × (3.15 × 10⁷) = 2.5 × 10⁸

My `diameter' (height), mass (weight), and age are:

	D_y = (6 ft) × (0.3048 m/ft) = (6 × 0.3048) m = 1.83 m
	M_y = (185 lb) × (0.454 kg/lb) = (185 × 0.454) kg = 84 kg
	A_y = 50 years

Dividing the Sun's diameter, mass, and age by my diameter, mass, and age, I obtain:

	D ÷ D_y = (1.39 × 10⁹ m) ÷ (1.82 m) = 7.6 × 10⁸
	M ÷ M_y = (1.99 × 10³⁰ kg) ÷ (84 kg) = 2.4 × 10²⁸
	A ÷ A_y = (4.5 × 10⁹ years) ÷ (50 years) = 9.0 × 10⁷

Note that the units cancel out, so the final numbers don't depend on the units used. I would have got the same final numbers with any choice of units, as long as I use the same units for myself and the Sun.

1. In which way are you most like the Sun?

I'm most like the Sun in terms of age; the Sun is only (only???) about 10⁸ times my age.

2. In which way are you least like the Sun?

I'm least like the Sun in terms of mass; the Sun is about 2.4 × 10²⁸ times my mass.

3. Are you surprised by your answers to the two questions above?

The fact that the Sun is `only' about 10⁸ times my age still seems amazing to me. I'm not surprised that mass shows the largest difference; for objects of similar density, mass is proportional to volume, and volume is proportional to the cube of diameter.

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

Last modified: August 30, 2006
http://www.ifa.hawaii.edu/~barnes/ast110_06/homework/disc01.html