My answer
I understand that there is still some gravitational potential energy between the asteroid and the planet even when they are very far apart, but it is very close to zero.
So, the short answer is that the potential energy of gravity does not represent the available energy of the universe. In fact:
- it can become negative and still be “available”, that is, convertible into kinetic energy
- (somewhat related) it is only defined up to an additive constant (like any other kind of potential energy), so its value does not represent anything physical. In particular, the value $0$ represents nothing special from the physical point of view, and is set somewhat arbitrarily (like the temperature $0\operatorname{° \!C}$, the calendar year $0$,…).
- in the mathematical model (not in reality), the total "available energy" that the gravitational attraction has is theoretically infinite assuming the two objects are point particles (*), because the potential energy does not have a minimum value and can reduce indefinitely. More precisely, two point particles with positive mass, under the gravitational force, are basically an infinite source of energy from the point of view of classical mechanics (point particles have no radius). That is admittedly mind-blowing and weird, but it is just a feature of the too simple mathematical model.
From this, the fact that the potential and kinetic energies at the initial time are zero is completely irrelevant to “the total energy of the universe” (whatever that is). It would be like watching your phone, noticing that we are in $2023$, and saying “Wow, the universe is just $2023$ years old! It is a very small time!”. It is just not what the date is meant to indicate… The calendar date (like the time on the clock, the Celsius and Farenheit scales, etc.) can be negative (before Christ) in the same way as the potential energy can become negative. And the calendar date is not “absolute” in the same way as the potential energy is not defined absolutely: it is defined only up to an additive constant. And it is not meant to indicate the amount of existing or “available” energy: it is just used to compute the work of the gravitational force, like we use the calendar to compute how much time has passed between two events.
Another example: there can be heat conduction from a source at $0\operatorname{° \!C}$ to another object at $-100\operatorname{° \!C}$, despite the first "having zero temperature". This is because zero temperature does not mean zero available energy, and the temperature can go below zero (Celsius!). (the difference is that there exists a minimum temperature, while there does not exist a minimum gravitational potential energy, this is why the asteroid can theoretically gain infinite kinetic energy).
In short. Energy is not created from nothing; the fact that the initial energy is zero does not mean that "there is no available potential energy"; in fact it means nothing, sinice you can rescale the potential energy as you like by an additive constant. The actual strange feature is that there is no theoretical limit on how much potential energy can be converted into kinetic energy.
Below, many more details in case you want to dig a little bit deeper into the math and you feel like you need to read more.
(*) In practice, though, if the two bodies have positive radii, the distance between the two centers of mass cannot become less than the sum of the radii before the collision, hence the potential energy cannot really drop to $-\infty$ (see the last part of the answer for the details). I would say, the available energy is theoretically infinite, but practically finite, because the limit depends on how large the asteroid and the planet are, not on anything “fundamental” or fixed, like their masses. (With more sophisticated physical models, the total available energy is likely not even infinite in the first place, but one would have to take into account general relativity, event horizons,… It becomes really messy.)
Many more details
The potential energy is defined up to a constant
In the case of gravitational attraction, it is a very standard thing to do to set the additive constant in such a way that the potential energy approaches zero when the bodies are very far apart: that is, we set the potential energy $U$ as
$$ U(r)=-\frac{Gm_1m_2}{r}, $$
(here $m_1,m_2$ are the two masses, $G$ is the universal gravitational constant, $r$ is the distance between the two objects’ centers of mass). But it would be perfectly fine to add any fixed constant to the potential energy: the quantity
$$ \widetilde U(r)=-\frac{Gm_1m_2}{r}+ 75400,86\operatorname{Joule} $$
is still a perfectly valid and usable potential energy for the gravitational force. We can use both potential energies in our physics computations, because what really matters is always $\Delta U=U(t_2)-U(t_1)$, i.e., differences of potential energy at two different times, not the specific value of the potential energy (when you take differences, any additive constant (like $75400,86\operatorname{Joule}$) cancels out, that is, $\Delta U=\Delta \widetilde U$). Recall that $-\Delta U$ coincides with the amount of work $W$ produced by the force between the times $t_1$ and $t_2$: the potential energy is just a mathematical tool used to compute the amount of work produced by the force. This is why $\Delta U$ matters more than the actual values of $U$. The actual values of the function $U$ represent nothing physical.
So, it makes no sense to say that the energy at initial time is “small”. The potential energy approaching zero when two bodies are far apart does not mean that the universe has no available energy. In fact, it is perfectly fine that the potential energy becomes more and more negative, while the kinetic energy grows (positive). Once you understand this, I write below some more comments.
Fun fact (before we continue). If the planet has radius $R$, then there is another very natural choice to define the potential energy:
$$ U(r)=-Gm_1m_2\left(\frac{1}{r}-\frac{1}{R}\right)= \frac{Gm_1m_2}{R}\left(1-\frac{R}{r}\right). $$
That is, you define it to be zero when $r=R$: you consider the asteroid to have $0$ potential energy when it lies precisely on the surface of the planet. Now you can call $h:=r-R$ the height of the object with respect to the surface, $g:=m_1G/R^2$ the gravitational acceleration on the surface (for the Earth, $g=9,8\,m/s^2$). If you assume that $h$ is small compared to $R$ so that you can approximate $1-R/(h+R)=h/(h+R)\sim h/R$, you obtain a very familiar expression for the gravitational energy:
$$ U(r)\sim m_2gh. $$
Potential energy can become negative... And it is not particularly remarkable. The remarkable thing is that it does not have a minimum value
The “total energy of the universe” at initial time and right after you change the direction of the asteroid is essentially the same, because the potential energy is unchanged as well as the kinetic one. And the energy is conserved after that time, all the way to the impact. In short, energy is conserved throughout the whole process.
So, if you think “wow, during the impact I see a lot of energy”, then be sure that the universe already had that energy even before you changed the direction of the asteroid, because energy is conserved. You don’t see it in the potential energy, because the potential energy is not meant to indicate the absolute amount of energy that is available and that can be converted in other forms of energies. Very often this is the case (e.g., the potential energy of a spring), but it is not the case for gravity: even if the initial potential energy is zero, potential energy can be spontaneusly converted into kinetic energy (of course, making the potential energy negative).
The source of your confusion is mainly in the fact that the potential energy of the gravitational force can be negative, so it is not clear how much available energy it possesses. I will tell you more: there is actually no theoretical limit to how negative it can get, and to the amount of energy that can be converted into kinetic energy. The fact that the potential energy can be negative is something that cannot be changed by adding a constant to it, since adding any constant to the potential energy would never be able to make it positive for all values of the distance between the two bodies (the function $ U(r)=-\frac{Gm_1m_2}{r}+c $ will never be positive for all $r$, for how large you choose the additive constant $c$). In other words, the potential energy $U$ is unbounded from below. This feature also implies that, in theory, the asteroid could gain an arbitrarily high kinetic energy if it comes close enough to the planet (in practice this is prevented from the fact that both bodies have a finite radius, so their centers of mass cannot have arbitrarily small distance).
Final note: the energy released from the impact
If we assume the two bodies have radii $r_1$ and $r_2$, and even if we assume they are infinitely far apart, the energy released from the impact will be roughly
$$ W=-\Delta U=-(U(r_1+r_2)-U(\infty))=\frac{Gm_1m_2}{r_1+r_2}-0 =\frac{Gm_1m_2}{r_1+r_2}. $$
This means that you don’t really have a way to make the impact more and more violent by putting the two bodies far and far apart at the initial time, and if the radii are non zero there is in practice an upper bound to the energy that can be released from the impact (assuming there is no, or very little initial kinetic energy).
It also means that the potential energy, in practice, does not drop to $-\infty$ at the moment of collision, and if it did that, the kinetic energy will become $+\infty$ (unlike what you wrote above). As I said before, if you just look at the math and you assume that the two objects are point particles (no radii), and if the asteroid heads precisely towards the planet, then during the collision, the kinetic energy does indeed blow up to $+\infty$, and the potential energy drops to $-\infty$. It is essentially like the total energy of the universe is infinite.
