# Answer 1. The Sun & You

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

 DY = (6 ft) × (0.3048 meters/ft) = (6 × 0.3048) meters = 1.83 meters MY = (165 lb) × (0.454 kg/lb) = (165 × 0.454) kg = 75 kg AY = 43 years

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

 DS ÷ DY = (1.4 × 109 meters) ÷ (1.82 meters) = 7.7 × 108 MS ÷ MY = (2 × 1030 kg) ÷ (75 kg) = 2.7 × 1028 AS ÷ AY = (4.5 × 109 years) ÷ (43 years) = 1.05 × 108

Note that the units cancel out, so the final numbers have no units attached. These quantities are `pure' numbers, independent of the system of units. 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 am I least like the Sun?

• I'm least like the Sun in terms of mass; the Sun is almost 3 × 1028 times my mass.

2. 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.

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

• The fact that the Sun is `only' about 108 times my age still seems amazing to me -- it makes me think that we can almost comprehend the vast times involved in astronomy. 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)