Kinetic energy of meteoroid falling from rest at infinity

[spinnaker]

Hi there,

I'm helping tutor a friend in astrophysics and I've come across a question I can't answer - which is annoying and embarassing to say the least :)

The question reads:

(a) Calculate the kinetic energy and pressure involved when the Earth gets hit by a stony meteoroid (ρ = 3400 kg/m³) that has a diameter of 10km and a zero velocity at a very large distance from the Earth.

(b) Calculate the kinetic energy and pressure involved if the same meteoroid were to hit Jupiter instead of the Earth, assuming the body has zero velocity at a large distance from Jupiter

(c) Calculate the kinetic energy and pressure involved when a fragment of Comet D/Shoemaker-Levy 9 (ρ = 500 kg/m³, R = 0.5km) hits Jupiter at the planet's escape velocity.

My problem is the zero velocity at a very large distance from the Earth. I can't figure out a reference point from which I can calculate total energy -- 1/2mv^2 means nothing at zero velocity, and "large distance" tells me nothing for calculating total energy.

Any help/hints/tips would be appreciated!

 

[tms]

My problem is the zero velocity at a very large distance from the Earth. I can't figure out a reference point from which I can calculate total energy $\ldots$

In cases of gravitation, it is usual to pick the zero point of potential energy to be at infinity.

$\ldots$ -- 1/2mv^2 means nothing at zero velocity,

Having a value of zero is not the same as meaning nothing.

 

[spinnaker]

Fair enough, I've been tinkering and I think I found my initial issue. I made 0 = 1/2mv^2 -GM(earth)m(asteroid)/r(earth) and I get 8.88e23 J, which is realistic. Equates to an impact of about 11km/s.

I still don't know what they mean by pressure involved, though.

 

[tms]

I'm not sure what they want for the pressure, either. Obviously the force per unit area of the collision, but which area? The entire cross-sectional area of the Earth, or just the immediate area of the impact? I would guess the former, but I'm not positive.