Energy in different inertial frames

[Oliver321]

Lets neglect conservation of momentum and assume that all frames of reference are inertial. Now imagine three objects: the sun, the Earth and an asteroid. In the inertial frame of the sun, Earth and asteroid are flying towards each other ( velocitys v and -v).
Now imagine you are standing at the surface of the earth: you see the asteroid flying towards you with 2v. So after some time the asteroid hits the Earth and all of its kinetic energy (K=2mv^2) gets converted into thermal energy (let’s assume the Earth stands still after the impact which implies that also the asteroid stands still). The temperature of the Earth rises.
Now look at this scenario from perspective of the sun:
Earth hast velocity -v and the asteroid has velocity v (so a velocity difference of 2v). They both hit each other. In the first moment the asteroid gets slowed down to zero (converting its kinetic energy in thermal energy) and in the exact same moment the asteroid gets accelerated to the velocity of the Earth (which costs energy). But that would implie that really no kinetic energy gets converted into thermal energy, because the kinetic energy of the Earth and the asteroid are the same before and after the impact. Only the velocity of the asteroid points in the other direction. Nevertheless kinetic energy could not be negative so the direction plays no role.

Where is my mistake?

Thank you for your help!

 

[PeroK]

If momentum is conserved, then the change in kinetic energy is the same in all frames.

Ignoring momentum is your mistake.

 

[Oliver321]

If momentum is conserved, then the change in kinetic energy is the same in all frames.

Ignoring momentum is your mistake.

But shouldn’t it be, that energy for its own is conserved? Is there something that connects energy and momentum deeply? I thought both conservation laws arise from different properties of our universe (noether theorem).

 

[PeroK]

But shouldn’t it be, that energy for its own is conserved? Is there something that connects energy and momentum deeply? I thought both conservation laws arise from different properties of our universe (noether theorem).

Energy is conserved but not kinetic energy alone. Kinetic energy may be converted to thermal energy for example.

Special relativity unifies energy and momentum in a beautiful way.

 

[A.T.]

Lets neglect conservation of momentum and assume that all frames of reference are inertial.

How do you define "inertial frame of reference", if conservation of momentum doesn't apply?

 

[Oliver321]

Energy is conserved but not kinetic energy alone. Kinetic energy may be converted to thermal energy for example.

Special relativity unifies energy and momentum in a beautiful way.

So I don’t get a right result if I don’t consider momentum?

How do you define "inertial frame of reference", if conservation of momentum doesn't apply?

That’s a good question. That’s probably not possible. Nevertheless it is a bit confusing for me, that I can not get the right awnser without respecting conservation of momentum.

 

[PeroK]

So I don’t get a right result if I don’t consider momentum?
That’s a good question. That’s probably not possible. Nevertheless it is a bit confusing for me, that I can not get the right awnser without respecting conservation of momentum.

If an asteroid hits the Earth then that is a totally inelastic collision. Kinetic energy is lost. Using conservation of momentum tells you how much kinetic energy is lost.

If you do not consider momentum then you do not know the final velocity of the Earth after the collision.

 

[A.T.]

Nevertheless it is a bit confusing for me, that I can not get the right awnser without respecting conservation of momentum.

First you have to ask a question that is not self-contradictory.