Fictional physics problem -- Firing projectiles into Earth orbit

[Umair Shariff]

Hi guys, I've recently been reading a lot of Jules Verne and I had a few curiosities that you guys could help with.

First, if we were to shoot or fling a bullet to low Earth orbit, what would the muzzle velocity have to be??

Second, instead of a bullet, if we used a capsule with one passenger in it and nothing else, what would the g forces that the person would endure??

Third, I understand that the escape velocity of the Earth is at 11.2 km per s, would that value change if we were to change the height of launch, like the top of Mt Everest??

Fourth, assuming that we successfully developed protocols to shoot a projectile into low Earth orbit, what would be the result of the drag forces on the projectile??

I would appreciate the help of the guys and girls of the physics community to help me understand more about the limitations that surround us.

 

[jedishrfu]

Wikipedia has an article on Escape velocity:

https://en.wikipedia.org/wiki/Escape_velocity

The formula provided is dependent on the distances from the center of the Earth to the object so in answer to your question it will change with height. The higher you launch from the lower the velocity.

For a spherically symmetric massive body such as a star or planet, the escape velocity for that body, at a given distance is calculated by the formula

where G is the universal gravitational constant (G = 6.67×10−11 m3 kg−1 s−2), M the mass of the body to be escaped, and r the distance from the center of mass of the mass M to the object.The relation is independent of the mass of the object escaping the mass body M. Conversely, a body that falls under the force of gravitational attraction of mass M from infinity, starting with zero velocity, will strike the mass with a velocity equal to its escape velocity.

 

[BvU]

Hi Umair, an amusing subject indeed !

First see here

Second: zero g when in orbit. It's launching that is the problem. You need a very long launch tube if you don't want to crush the passenger and still get the speed to 11200 m/s. Say you're prepared to risc 10 g -- you need 112 seconds (11200 m/s divided by 10 m/s²) and with $s = {1\over 2} a t^2$ that's 630 km !

Third: there's a $1/\sqrt R$ in the expression, so 5 km on 6000 km doesn't make more than 5 m/s difference in the escape velocity

Fourth: I think the 'flight' would be very uncomfortable. Probably very hot too, and ending with a crash.

 

[sophiecentaur]

Something needs mentioning here. If you fire a projectile into space with less than the 'escape velocity' it will not go into orbit but crash back to Earth. It's first and only orbit will take it through the Earth's surface. You need another impulse when it is high enough to make the orbit more circle like. That will then avoid a collision with the ground.
A'gun' launch will only work when the projectile can escape Earth's gravity completely. All real launches have a correcting boost to achieve more than one orbital cycle.

 

[nasu]

You don't need escape velocity to launch a projectile in low Earth orbit. You just need the orbital speed required by the desired orbit.
This will not be same as muzzle velocity, which need to be much higher in order to compensate for air resistance.

 

[BvU]

You don't need escape velocity to launch a projectile in low Earth orbit. You just need the orbital speed required by the desired orbit

Oops, nasu is right of course. At Earth level a factor $1/\sqrt 2$ less. A respectable speed required remains, however.

 

[Khashishi]

The g force will depend on how long the launch tube is. A longer launch tube is better.
Secondly, it won't actually work. The air resistance is too high to fire something into space this way. Even a streamlined capsule will have too much drag. That's why we use rockets instead of cannons to go to space.

(Note that the inertia to drag ratio increases with the size of the projectile, so for a sufficiently large bullet of dense material, the the drag could perhaps be low enough for this to work. How large a bullet?)

 

[sophiecentaur]

. . . and a simple projectile will not have an orbit with low enough eccentricity to stay up there.
The air resistance factor is interesting. Even heat generation would be significant. It is even relevant in normal supersonic flight.
The idea in this thread, in its simplest form is really a dead duck.
"I want to do it this way" is never a good reason for a choice of method.

 

[nasu]

Well, he said "a fictional..." :)

 

[sophiecentaur]

True. But we have come a long way since J Verne.