Even if you were to just drop the bullet, anything dropped from that height will be going extremely fast by the time it reaches the surface. Very nearly escape speed, in fact.
You shoot the bullet away from the Moon. Without an atmosphere, it’s basically just gravity affecting the bullet’s path. It will go slower and slower as it rises away from the moon, just like if you throw something straight up in the air on the earth - it goes slower and slower then falls back down. Except that you’ve thrown it so hard that it won’t come back down.
So the bullet keeps going slower and almost stops, and then the gravity of the earth becomes more dominant than the gravity of the moon, and the bullet starts accelerating towards the earth. It has a VERY long time to accelerate, and no atmosphere to slow it down while it is way out there, so it accelerates to a very high velocity. I’m not going to do the math to figure out exactly how fast it will be going when it hits the atmosphere, but it’s going to be pretty darn fast.
The bullet will have a specific energy somewhere on the order of 0.5 MJ/kg. Assuming that it is on a direct intercept course and you can neglect lateral motion (otherwise, it will just shoot past the Earth on a high elliptical orbit) you can estimate the speed by subtracting the gravitational potential specific energy at whatever altitude you like and taking the square root of 2 times the remainder. I can pretty much guarantee that a bullet made out of copper-jacketed lead or steel will vaporize long before it gets to the surface. A bullet with a tungsten core may get further, but I wouldn’t expect enough accuracy to even hit a particular city, much less an individual target.
Stranger
It would be going faster than on earth since in order to be fired from the moon it would have to achieve escape velocity (or, at least escape the moons gravity well AND fall into the earths) from the moon. A quick Google search shows the escape velocity of the moon at 2.4km/s…the fastest bullet I could find on Google is 1300m/sec. (rail guns can go faster, but they use special alloys and very small projectiles to avoid burning up). The Apollo capsule didn’t burn up because it had an ablative coating on the bottom of it and it hit at an optimal angle. A bullet though I don’t believe would make it.
The Apollo capsules did burn up on re-entry. They just didn’t burn up completely. The crew compartment, and the crew inside, were intact, but the heat shield gets pretty badly pitted and scarred, and the thickness of material that’s removed is more than the size of a bullet.
You can figure a rough approximation of the bullet’s speed by taking the high school physics “assume a spherical cow” case of a bullet on a parabolic arc at just under escape velocity (ignoring atmospheric friction and pretty much everything else except gravity, hence the assume a spherical cow). At the top of the arc the speed will be very close to zero, and at the bottom of the arc on both the way up and the way down the speed will be just under the escape velocity. Now push it a bit over escape velocity and you can get to the moon. Reverse that, and the bullet comes down at just over the earth’s escape velocity. This is obviously a gross oversimplification, but it will give you a rough answer for the bullet’s speed.
So figure roughly around 11 or 12 km/s when the bullet hits the atmosphere, or just a bit higher than the speed of the Apollo spacecraft when they hit the atmosphere (they were around 10 km/s or so).
And to put it in perspective, your typical meteor is going to be somewhere around 10 to 50 km/s. Your bullet is right up there in the same ballpark.
Which is, of course, its function. The ablated material becomes part of the hot gas that both provides sustains a standoff shock wave (which prevents direct contact of the hot gas to the capsule, limiting heating to the back radiation at the shock front) and actually provides cooling. One of the major showstoppers in developing a truly reusable space vehicle is a reentry thermal protection shield that is robust and can survive many reuses before replacement. Active cooling via heat exchangers under the the primary thermal surfaces is probably the only genuinely viable solution, but the required reliablity of such a complex yet extensive system defies practical design.
Stranger
Sounds like a job for an AK47. Who knew the Russians were planning for Lunar warfare that far back!
Someone else asked about a ceramic bullet. What if the bullet had a lead core for weight and a ceramic shell to withstand the heat?
They have a quarry on the moon?
What you need is a bullet made out of a mithril-adamantium alloy.
So what about an Iowa-class battleship on the moon? Could it hit the Earth? What would its range on the Moon be?
The 1964 Ben Bova short story “Men of Good Will” dealt with the aftereffects of a gun battle on the moon between the Russians and the Americans. Most of the bullets missed, and ended up in orbits that have their periluna at the same place they were fired from every 28 days. So on that day, everyone has to take cover lest they get shot again. It takes all the computing power available just to track the bullets in orbit - they can’t shoot any more or the computers will be overwhelmed.
Whether or not it’s scientifically accurate, it’s a dryly funny story.
maybe xkcd what if can do the math on this
According to wikipedia, the muzzle velocity of the 16 inch guns on an Iowa class battleship is 762 m/s, which is too low to escape the moon’s gravity. The shell will just end up back on the moon at some point.
The guns have a range of 38 km. The moon has about 1/6th the gravity of the earth, so the guns would have a range of roughly 6 times that, or 228 km.
Duly acknowledged in Rip Foster Rides the Gray Planet, which fell far short of scientific rigour in many respects but did acknowledge that a knife slash to a spacesuit guarantees instant surrender. The author possibly overstated the unpleasantness of an actual wound in such circumstances but it wasn’t bad for 1950s science fiction.
Hmmm. I wonder what the initial speed would need to be for the Iowa to blow itself up? Not escape velocity but enough so its trajectory would take it around the moon to drop the shell right back on its point of origin.
I am none too clever so I suspect this is complete rubbish but I will put it out here to encourage more sophisticated minds to correct the worst scientific atrocities I am committing.
The average distance from the Moon to the Earth is 384,400 Km but that is measured from a theoretical centre of the Earth and Moon. Since the Earth and Moon have diameters of about 12,752Km and 3,474Km then those added and halved means the distance from the average surface of the Moon to the average surface of the Earth is reduced from 384,400Km to just 376,292Km.
Now for what even I know are massive assumptions. Since current sniper rifles have less than the escape velocity on the moon I will assume the next generation of sniper rifles have exactly the escape velocity of the Moon: 2,380m per second. I will make the unlikely assumption the bullet is being fired in a straight line and the average velocity is set at escape velocity.
So 376,292,000m at 2,380m per second will take 158,106s or 2,635 minutes or 43.9 hours or one day and 19 hours. So the concept of looking through an optical telescopic sight directly at the target is ludicrous.
I wait to see whether I have misplaced a decimal point somewhere.
TCMF-2L
In that case, the bullet will get to about 1/6th of the way toward earth, the exact location is really not important to calculate , and then forever remain in Sol orbit. Its speed toward earth would be 0.00000 metres per second, because the moon’s gravity pulled off it the escape velocity…
The escape velocity is a measure of the depth of the ‘gravity well’… what speed you need to get out… And how much speed you lose getting out…
OK. So would an average velocity of six times the escape velocity get the bullet to Earth?
Assuming my other calculations are correct that would still give a travel time of seven and a half hours.
TCMF-2L