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# Section 1.2 Large and Small are Relative

We noted that one light-year is about 12 million trips to the moon and back. But one light-year is also

• about $\frac{4}{17}$ the distance to Proxima Centauri, the nearest star to Earth outside our solar system.
• approximately $\frac{1}{106\,000}$ the width of the Milky Way (the galaxy containing planet Earth).
• approximately $4.6 \cdot 10^{-10}$ (one forty-six-billionth) the distance from earth to the edge of the visible universe.

As we said, large quantities are large compared to smaller quantities, but large quantities can be very small when compared to much larger quantities.

## Exercise Set 1.2

Use GC for your computations. Enter "*" for multiplication, "/" for division, shift-6 ("^") for an exponent, "$\downarrow$" to exit an exponent, "$\rightarrow$" to move to the next term.

You might be tempted to use your personal calculator for these exercises. PLEASE DON'T DO THIS. Use GC. It is by using GC that you will become comfortable using it. Being comfortable with GC will be very important for later chapters.

1. As of 2010, the smallest time interval that can be directly measured is approximately 12 attoseconds ($1.2 \cdot 10^{-17}$ seconds). What, then, is the smallest possible distance that can be directly measured with a laser?
2. The volume of an average-size human body is 66.4 liters ($0.0664 \mathrm{ m^3}$). The volume of an average-size human cell is approximately $1.1 \cdot 10^{-15} \mathrm{m^3}$. Use this information to estimate the number of cells in an average-size human body. (Data derived from Wolfram Alpha and Bianconi et al., 2013.)
3. In 1989, Admiral Grace Hopper, inventor of programming languages, handed out nanoseconds to members of her audience. The nanoseconds she handed out were pieces of wire whose lengths were the distance light travels in one billionth of a second. How long were these pieces of wire?
4. You have watched television news reports from a reporter who is on the other side of the earth from the newsroom. The reporterâ€™s image and voice is being transmitted by satellite. The orbit of communication satellites is approximately 23,000 miles from earthâ€™s surface. What is the shortest delay you could expect between seeing a news anchor finishing a question and seeing the distant reporter beginning to reply?
5. Information: The diameter of a carbon atom is about $2.20 \times 10^{-8}$ cm. The distance from Sun to Earth is approximately $1.49\times 10^8$ km. The distance from Sun to Proxima Centauri is approximately 4.22 light-years.

Draw a 10 cm line segment. Suppose this segment represents the distance from Sun to Proxima Centauri.

1. How far along your line, in carbon-diameters, would be the distance from Sun to Earth?
2. The New Horizons space probe is the fastest spacecraft ever launched. It traveled at 58,536 km/h. How far along your line segment, in cm, would the New Horizon probe be after 10 years?
3. What does your answer to Part (b) imply about the possibility of sending a space craft to Proxima Centauri using existing technology?

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