Collision: Earth Orbit

Carolyn

The question is

If after Halley's comet hits the earth, the earth continues to move in its initial direction but with a greater speed (1.12 times) , find the new semi-major and semi-minor ases of the new earth orbit in terms of the original R.

So, my question is, do you think that the angular momentum of the earth is conserved in this process? or is R conserved in the process( which means R does not change)?

The question assumes that the earth is initially moving in the circular orbit, then after the collision it moves in a elliptical orbit.

Thanks for any help!

Tide

Why would you think R is conserved?

HallsofIvy

Why would you think that angular momentum of the earth is conserved if there was an outside force (the collision of the earth with a comet)?
If the earth's speed, v, becomes 1.2v, then its square becomes 1.44v² so the the earth's kinetic energy is increased by a factor of 1.44. Of course, the potential energy, at that point, is still the same so the earth's total energy has changed.

Mike2

If the velocity increases by 1.12, then the Kinetic energy increases by the square of that. How much farther will the earth have to travel out from the sun until its potential energy equals newly acquired kinetic energy? You'll have to do a diff eq of the forces involved given the new initial conditions of the added speed and initial tangential direction. Given the initial conditions of the location and direction of velocity, the acceleration is equal to the forces on the earth divided by the mass of the earth.