Question

It’s estimated that there are a trillion comets in the Oort cloud, which extends out to about 50,000 AU.How much space does each comet have in cubic AU, on average?

2. Take the cube root of the average volume per comet, to find their typical spacing in AU.

3. A relatively small impact crater 20 kilometers in diameter could be made by a comet 2 kilometers in diameter traveling at 31 km/s (3.1×104 m/s ).Assume that the comet has a total mass of 4.2×1012 kilograms. What is its total kinetic energy? (Hint: The kinetic energy is equal to 12mv2, where m is the comet's mass and v is its speed. If you use mass in kilograms and velocity in m/s, the answer for kinetic energy will have units of joules

Answer 1

1. Each comet has 523 UA³
2. The typical spacing would be 8.05 UA
3. 2.0181x10^21 Joules

Step-by-step explanation:

1. Assuming comets are evenly distributed we can find first the volume of a sphere with the formula frac{{4}{3}}πr³ using 50000 as the radius, and then dividing this volume by the amount of comets. This gives a the space each comet has on average.
2. We apply the cube root as proposed in the question.
3. The kinectic energy is given K=frac{{1}{2}}mv² where m is the mass and v is the velocity. Apropriate unit are given in the question.