Geo 147, The Impact Problem

Due: Thurs, April 4, 1999

Background

Impacts are an important process in our Solar System, and
there is evidence on our plnaet and others that impacts continue to occur, albeit at a slower rate than in early history.
Furthermore, it is now a popular notion that rare large impacts may be responsible for mass extinctions on Earth.
Thus, we will calculate some of the energy and effects of a moderately large impact event.
It is easy to estimate the total energy of an impact using the formula for gravitational potential energy, so that's where we'll start...
- If we have an object with mass of M that falls to the Earth's surface from infinity, then the gravitational potential energy of the object when it is far away from the Earth is: Ep = g M R
  where g is the gravitational accleration at the Earth's surface ( about 9.8 m/s^2, where "s^2" reads as "seconds squared"), and R is the Earth's radius (6371. km).
- Also, remember that kinetic energy of a moving object is given by: Ek=(0.5)MV^2
  where M is the mass of the object and V is its velocity.

The Problem

Energy

1. Lets do our calculations for a spherical meteorite with a radius of 50 meters. Your book says that we should expect one of this size to hit the Earth every 10,000 years. Suppose that it is a rocky metoerite, with a density of 3. x 10^3 kg/m^3. Calculate the mass of this meteorite.

2. Now,use the above formula to calculate the potential energy of the meteorite before it falls to Earth. (The units of energy should be Joules).

3. Now, lets suppose that the meteorite has a "zero initial velocity with respect to the Earth" when out in space. The only point here is that the incoming velocity of the meteorite just before it strikes the Earth's surface is then given by equating the potential energy to the kinetic energy. Do so, and calculate V, the velocity, at the Earth's surface, ignoring friction and any other effects. (units should be km/s). Compare this velocity to something else so that we may know whether it is fast or slow.

Energy Conversion

4. Earthquakes: If all of this incoming energy were converted into seismic waves, then the magnitude of the equivalent earthquake is given by the formula: M= -3.1 +(0.667)log E, where E is the energy in Joules.
Calculate the magnitude for your impact. Is this a large earthquake? Would seismologists notice this event, even if it occurred in the middle of nowhere?

5. Heating: If all of this incoming energy were converted into heating, we can calculate the temperature increase if we just know the mass of material that is heated. Lets suppose that this object heats up Lake Michigan. Estimate the water volume in Lake Michigan (doesn't have to be too precise, e.g. approximate Lake Michigan as a rectangular box). Then use the density of water (10^3 kg/m^3) to get the total mass. To convert an energy input into the temperature, we need the physical property of "specific heat", which is about 4.2 x 10^3 Joules/(kg deg) for water, where "deg" is degrees Kelvin. So, what is the temperature increase? Is this a lot? Would we notice it?.

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