5. An astronomical unit (AU) is the average distance of the earth from the sun, approximately \( 150,000,000 \mathrm{~km} \). The speed of light is about \( 3 \times 10^{8} \) \( \mathrm{m} / \mathrm{s} \). Express the speed of light in terms of astronomical units per minute.

To express the speed of light in astronomical units per minute, first convert the speed of light from meters per second to kilometers per minute. So, \( 3 \times 10^8 \) m/s equals \( 3 \times 10^5 \) km/s, and in a minute (60 seconds) that's \( 3 \times 10^5 \times 60 = 1.8 \times 10^7 \) km/min. Now, since 1 AU is approximately \( 150,000,000 \) km, we can calculate \( 1.8 \times 10^7 \) km/min as: \[ \frac{1.8 \times 10^7 \text{ km/min}}{1.5 \times 10^8 \text{ km/AU}} \approx 0.12 \text{ AU/min}. \] So, the speed of light is approximately \( 0.12 \) AU/min. Ever wondered how small our solar system is in the grand scale of the universe? The nearest star system, Alpha Centauri, is about 4.37 light-years away, which translates to around 277,000 AU! To put that in perspective, light took over 4 years to travel from there to us. It's fascinating to think about the vast distances between celestial objects and just how mind-bogglingly fast light travels relative to those expanses! If you find yourself struggling with unit conversions, a common pitfall is overlooking the scale of the units involved. Begin by establishing clear conversion factors and use them step-by-step. For example, ensure you know how many seconds are in a minute and how many kilometers are in an astronomical unit. Double-check your calculations as you go, and don't be afraid to break it down into smaller parts!