[Petrochemicals (OP)]

A piece of space rubbish is going to impact the moon.

https://www.bbc.co.uk/news/science-environment-60596449

I believe it takes a lot of energy to get from near earth orbit to the moon, how did it gain the energy, or if it is part of a moon rocket I thought the idea of rocket stages where that the release of a stage meant you gained  energy to get to the moon, equal and opposite and all.

[Janus]

The stage separation adds nothing to the energy of the craft.  It is merely done to shed excess mass(empty fuel tanks and superstructure) that will just get in the way during later maneuvers.
For example, by the time the third Apollo stage separated from the rest of the craft the whole assembly had already achieved the velocity needed to reach the Moon.  The stage is then  jettisoned so that its mass isn't a factor during the Lunar Orbital Insertion burn needed once the craft arrived at the Moon.
The jettisoned third stage still has enough velocity to continue on the the Moon after separation(just on an slightly altered course than the rest of the craft.)

[evan_au]

The rocket booster that hit the Moon was initially thought to be a SpaceX booster.
- SpaceX doesn't just launch satellites into Low Earth Orbit (eg the thousands of Starlink satellites, or supply missions to the ISS). As you say, these would not have the energy to reach the Moon, but would fall back into Earth's atmosphere and burn up.
- SpaceX also did a publicity stunt, where the launched a Tesla car out past the orbit of Mars. Debris from this launch definitely had enough energy to reach the Moon.

However, the booster thaht hit the Moon has now been identified as one from the Chinese Chang’e 5-T1 Moon mission. This rocket boosted a probe to the Moon, so the booster has enough energy to reach the Moon.

https://skyandtelescope.org/astronomy-news/booster-set-to-hit-the-moon-turns-out-to-be-chinese-rocket-not-spacex/

[Petrochemicals (OP)]

Does all this mean the ro ket stage was orbiting the moon from the point of release or was it just a lucky hit due to its impetus?

I had imagined some sort of billiard ball collision between it and something else, perhaps an asteroid and perhaps sling shot, or a secret spacecraft, or perhaps aliens.

[Petrochemicals (OP)]

Does all this mean the ro ket stage was orbiting the moon from the point of release or was it just a lucky hit due to its impetus?

If it orbited the moon, it could not have hit it. So it was in orbit about the Earth, in an orbit that crossed the lunar orbit. All it needed to wait for is for both objects to be at the intersection point at the same time, which is inevitable so long as the orbits are not altered.
Impetus is an artifact from pre-Newtonian physics. It was falsified centuries ago.

Nothing in orbit around earth has ever impacted the earth? Nothing can orbit the moon that itself is orbiting the earth?

[Halc]

Nothing in orbit around earth has ever impacted the earth?

Not without application of force to reduce its orbital energy. Hence retro thrusters on any orbiter returning to Earth, and friction of the upper atmosphere which degrades the orbit of anything that gets close (within 1000 km) of Earth.  The moon has no atmosphere, so something can in principle orbit 10 meters up and still never hit it.

Nothing can orbit the moon that itself is orbiting the earth?

There are three body orbital solutions, but not stable ones.

[Petrochemicals (OP)]

Nothing in orbit around earth has ever impacted the earth?

Not without application of force to reduce its orbital energy. Hence retro thrusters on any orbiter returning to Earth, and friction of the upper atmosphere which degrades the orbit of anything that gets close (within 1000 km) of Earth.  The moon has no atmosphere, so something can in principle orbit 10 meters up and still never hit it.

Nothing can orbit the moon that itself is orbiting the earth?

There are three body orbital solutions, but not stable ones.

So yes they can, to both points.

[evan_au]

A rocket that is launching a probe to the Moon needs to put the probe (and itself) into an orbit which has an apogee (farthest distance from the Earth) that is around 370,000km (the Moon's average distance from the Earth). But you don't want to aim for the visible center of the Moon (or your rover will crash at high speed, and not rove very far). You want to miss the Moon slightly, so the probe can enter Lunar orbit (by the smaller probe firing it's smaller rockets).

Now the booster is in a very elliptical orbit that has an apogee (farthest distance from Earth) of around 370,000km, and a perigee (closest distance from Earth) that is in Low Earth Orbit, perhaps a few hundred km, and an orbital period of a few weeks. If the operators are responsible, they will give the booster another boost when it is out near the Moon to (1) use up all the fuel in the tanks, so it doesn't explode and spread shrapnel into low earth orbit and (2) increase the perigee so that it doesn't come zipping past the ISS and other valuable satellites every 2 weeks.

So you now have a rocket booster in a very elliptical orbit around the Earth  every few weeks, reaching out as far as the Moon; and the actual Moon passing through the path of that orbit about every 4 weeks. Sooner or later, their paths are likely to cross, and in that encounter, the Moon comes off in better shape than the rocket.

Before there is an actual crash, there will probably be several near-misses (including the first, intentional near-miss), and some of the Moon's momentum is transferred to or from the rocket body; the Sun's gravity and solar wind also push around the booster (which is now basically a large, empty, aluminium can). That puts the booster in a somewhat chaotic orbit, making it harder to trace back the orbit to its origin, or to pinpoint many years into the future exactly when it will crash into the Moon.

Oops! overlap with Halc...