### ASTR 220 - Collisions in Space

#### Homework 2 (12 points) Due Tuesday March 7 at the beginning of class

1. Demise of the Dinosaurs:
Summarize the theory that an asteroid impact triggered a global catastrophe roughly 65 million years ago. Describe the observations which support this hypothesis.

2. Kinetic Energy and Meteor Crater:
It is estimated that the body (asteroid) whose impact formed Meteor Crater, AZ was about 60 meters in diameter and its composition was most similar to an iron meteorite. Its velocity is estimated at 20 km/s. This impact formed a crater 1.2 km (0.75 miles) in diameter. For each of a-c, first use the kinetic energy equation
E = 1/2 M V2
to predict how the energy of motion of the impactor would be affected by the given change (i.e. increase/decrease by a factor of X -- find X). More energy means a bigger crater. (Only simple calculations are necessary; use the table on Handout #6 and the "Working with Equations" link on the web page if you need help.) You can check your answer by modeling each impact on the "Collisions with Planets" link from the class web page.
• a) how does the energy change if the velocity is 60 km/s (instead of 20 km/s)?
• b) what if the asteroid was 120 meters in diameter (instead of 60 meters)?
• c) what if it was a comet nucleus of density 0.75 grams per cubic cm (rather than an iron asteroid of density 7.5 grams per cubic cm)?

3. Escape on Foot
In a bizarre twist to your already hectic life, you find yourself the victim of an alien abduction. The aliens drop you off on a small comet (kindly providing a spacesuit with an unlimited air supply). As the comet approaches the sun, it becomes a rather unpleasant place to be, what with hot geysers of vapor blasting out of the surface without warning. You decide you'd like to leave. The equation for the escape velocity is
Vesc = (2GM/R)1/2.
On earth, Vesc = 11 km/s. But the comet is much smaller, and has a lower escape velocity. Use the following data to determine the speed necessary to escape from the comet:
G = 6.67 x 10-11 m3 kg-1 s-2 is Newton's constant of Gravitation,
M = 7.5 x 1012 kg is the mass of the comet, and
R = 1000 m is the radius of the comet.
Keeping in mind that the top speed a running human can achieve is around 10 m/s, can you escape the comet if you take a running leap?