Help With Conservation Of Energy Concept
Can someone help explain something to me.
In a situation of an asteroid heading straight towards the Earth, I'm trying to understand where the energy comes and goes (using just gravitational potential energy and kinetic energy). Consider the energy of the asteriod some distance away from the surface of the Earth, then just before impact.
I'm using the following equations:
Kinetic Energy = Ek = 0.5mv2
Gravitational Potential Energy = Eg = (GMm)/r
My question is that, ignoring friction/sound etc, initially the asteroid has a certain speed and thus a certain kinetic energy, simple to work out. It also has a gravitational potential energy based on G and the masses involved and the separation. However, as it gets closer, the force from the Earth increased, as the separation 'r' off the objects decreases, the gravitational potential energy increases. At the same time, as the force on the asteroid increases, we expect the speed to increase so in effect, both Ek and Eg are both increasing. If both are increasing, then where is the energy coming from.
Surely it should be Eearly = Ek + Eg = Elater = Ek + Eg
Can anyone give me a basic idea of where I'm going wrong with this idea please.