WELCOME TO MY ONLY WORLD, IT IS FULL OF SPACE JUNK
IF YOU DO NOT WAIT FOR THE COMPUTER TO GIVE YOU A DAMN FIRING SOLUTION BEFORE PULLING THE TRIGGER, AND YOU MISS, YOU'RE GONNA RUIN SOMEONE ELSE'S DAY, SOMEWHERE, SOMETIME!
CONSIDER THE FOLLOWING
"a body in motion will stay in motion, following a straight path at constant velocity, unless acted upon by an external force"
On Earth these external forces are very prominent, the friction with the floor and air, and the pull of gravity all act against the straight path and constant velocity. But in the vacuum of space there are not such strong interactions with the space medium or gravity. That's why the Voyager spacecraft started their journeys with curved paths which became flattened into straight lines the further they went from the Sun, away from it's influence, the external force of the Sun's gravity is weaker and weaker with distance.
In the case of small scale conflict on Earth's orbit, any missed projectiles will either fall back onto Earth, or enter into orbits or curved paths around the planet. If a projectile is fired from a satellite in the direction of travel its speed will be slightly higher than the satellite putting into a path of a higher intersecting orbit around Earth, in the case the projectile is fired contrary to the direction of motion, the bullet will fall considerably behind the original trajectory or even fall back to Earth.
The velocity necessary to escape a closed trajectory around Earth from 2000km above the surface is around 9,75km/s, way lower than at the surface where it is around 11,2 km/s, just because gravity weakens with the square of the distance. In a circular orbit, the object stays in orbit because both the forces pushing it away from Earth and gravity are in equilibrium, you can say that is the point gravity acts as a balanced centripetal force.
If we increase the mass of the planet by a significant amount but not the speed of the satellite, it will fall towards Earth, and if the contrary happens or the satellite increases velocity, its orbit will expand to the point of equilibrium again.
We can play around with this concept using incomplete Hohmann Transfer paths, Hohmann transfers are a type of maneuver in space navigation, it consists of two burns at opposites of an orbit, using the image above as reference, the initial orbit is the green one, a burn is done to push the apogee of the orbit up to the yellow path, and once reached the apogee, another burn is made to increase the craft's speed and thus expand the perigee up to the red path, by the end of the maneuver you have changed orbits entirely, and it can be done in reverse as well.
Since we are dealing with a projectile fired from orbit, this is an incomplete transfer, and thus we care only about the shape of the yellow path. I have tweaked a Hohmann transfer visualizer made by someone else on Desmos, so you can input an additional positive or negative velocity to the body in motion around the Sun, starting around Earth's orbit.
By inputting 300 m/s on projectile velocity we get a graph that looks like this:
Given that Earth's orbit is pretty circular overall, a body going at an extra 0,3km/s in its orbit around the Sun would have gone 0,068 AU (10 million km) further away than Earth over a period of six months. Had that speed gone over 1,2 km/s and the bullet is hitting some asteroid or probe 30 million km away, between Mars and Earth.
Now, we could argue that space is pretty empty and that it won't hit anything important in the mean time, but that projectile's orbit intercepts that of Earth's, so it is either going to fall onto the planet or be swung away by the planet's gravity. That is still a real bullet in space and it won't stop until it hit some debris along the way.
THE TRUE PROBLEM...?
We have to recognize that a single bullet may damage a satellite, or hit an already dead-weight piece of debris inside the lunar perimeter, or just never hit something really, given some rocks have been around for billions of years just now falling through Earth's atmosphere. But let me give you a number, 41,4 billion. That's the number of rounds fired by the US during WW2 alone, and it is estimated that between 40 and 50 thousand rounds were fired for each enemy taken by the US in both WW2 and Vietnam, that amounts to about 40 thousand shots hitting the ground, tanks, ships, and other infrastructure and landscape, none of which exists in space around Earth or known planets so far, and thus had WW2 have taken place in space around Earth, we would have toroidal zone of space around the Earth's orbit, 0,3 AU wide, infested with 41,4 billion projectiles and shrapnel still waiting to hit any target.
-M.O. Valent, 08/09/2022
