11.3  Describe the differences between a comet and a meteor in terms of size, distance, and how long they are visible.

Most meteors are dust-sized to pebble-sized grains burning up for a few seconds in Earth's atmosphere.  Comets are the product of the interactin of the icy surfaces of comet nuclei with the solar wind, often producing tails that stretch for millions of kilometers, lasting up to several months.
 

11.12  One recent estimate concludes that nearly 800 meteorites with mass greater than 100 g (enough to cause personal injury) strike the surface of Earth each day.  Assuming you present a target of 0.25 m² to a falling meteorite, what is the probability that you will be struck during your lifetime?

The radius of the Earth is 6.4 x 10⁶ m, giving a surface area of 4 x pi x r² = 5.15 x 10¹⁴ m².  Assuming you live 75 years,
800 x 365.25 days/year x 75 years = 2.19 x 10⁷ meteors will hit the Earth during your lifetime.

Divide the surface area by the number in 75 years to get one meteor per 2.35 x 10⁷ m² in 75 years.  If you take up an area of 0.25 m²,  your chance of being hit is 0.25 / (2.35 x 10⁷) = 1.06 x 10^-8, or one chance in 100 million.

I wouldn't worry, but every year you would expect about one person to be hit.

(Note - I wouldn't expect you to be able to do this problem on an exam.)

11.13  The orbital periods of comet Encke, Halley's Comite and comet Halle-Bopp are 3.3 years, 76 years, and 4200 years, respectively.

a.  What are the semimajor axis (in AU) of their orbits?

b.  What are the maximum distances from the Sun (in AU) reached by Halley's Comet and comet Hale-Bopp in their orbits.

c.  Which would you guess is the most pristine comet amoung the three of them?  Which is the least?  Explain your reasoning.
 

a.  Kepler's Third Law:  P² = D³

    Encke:  3.3² = 10.89  --  the cube root of which is 2.22 AU
    Halley:  76² = 5776 --  the cube root of which is 17.9 AU
    Hale-Bopp:  4200² = 17,6400,000 --- the cube root of which is 260 AU

b.  Since each comet comes very close to the Sun, their maximum distances are nearly twice the semimajor axes of their orbits.
      Halley:  36 AU
      Hale-Bopp:  520 AU

c.  Hale-Bopp is likely to be the most pristine, Encke the least.  The number of times the comets comes close to the Sun wears it down and the comet with the shortest period visits the most, the one with the longest visits the least.