Questions for curious engineers

[Toaster]

If we had the capability of giving enough momentum to a capsule to fly from Earth's surface to a 'safe' low stable orbit:

How high would that orbit be?

What initial position, shooting angle and trajectory would you choose? Given that the capsule can slightly modify its own trajectory once in the air.
We can set our 'magic gun' up to 6 kilometers over the sea level to avoid the thickest lowest part of the atmosphere and maybe save some energy there.

What initial (and final, once in orbit) speeds will the capsule need to be given at the surface? Given that there is no extra acceleration once the capsule is "shot", only fighting air drag and gravity on its way up, rotating around its axis like a bullet; while flying at supersonic speeds and slowing down.

Let's say the capsule is a very aerodynamic, supersonic bullet like shape with 2m in diameter, 10m long and weighs around 5-10 Tons.

How much temperature increase would it go through due to impacts of air particles at supersonic speeds?

Could we manufacture any materials that support those temperatures? In which particular configuration arrangement would they operate best to dissipate the heat?

If so, what materials should shell the capsule?

A source background would be appreciated.

 

[Bandersnatch]

Hi, welcome to PF.

If we had the capability of giving enough momentum to a capsule to fly from Earth's surface to a 'safe' low stable orbit:

It's not possible. If you don't allow the capsule to accelerate once it clears the surface, then it will not enter a stable orbit. The periapsis of its elliptical orbit will never be higher than the launch point, which means that the projectile will be slowed down by the atmosphere leading to a crash.

 

[Toaster]

The periapsis of its elliptical orbit will never be higher than the launch point

The capsule will use a small gyroscopes system to keep it in orbit, just like the ISS, but on a smaller scale.

 

[Bandersnatch]

Gyroscopes are used to adjust oritentation. They can't cause linear acceleration (due to conservation of momentum).
Your capsule needs a way to accelerate once it's high in its launch orbit, in order to raise the periapsis above the atmosphere.

 

[Toaster]

They can't cause linear acceleration (due to conservation of momentum).

They do not need to cause any extra acceleration. They start with all the initial velocity and then reach orbit. If this would not be possible, this would mean that I could through an un-breakable stone 500 x Earth's escape velocity and the stone would not escape Earth's gravity? Am I right?.

 

[jbriggs444]

They do not need to cause any extra acceleration. They start with all the initial velocity and then reach orbit. If this would not be possible, this would mean that I could through a un-breakable stone 500 x Earth's escape velocity and the stone would not escape Earth's gravity? Am I right?.

The original post asked for a safe, low, stable orbit. That would imply either a circular or elliptical orbit. With 500 times escape velocity, the rock would be following a hyperbolic trajectory instead. This is not what one would normally describe as a "low stable orbit".

Both circular and elliptical orbits are periodic. This means that you can extend the trajectory into the future and it will re-trace the same path repeatedly. As long as the craft is not accelerated out of this orbital trajectory, it is also periodic when looking into the past. A periodic, free-fall orbit which does not currently intersect with the atmosphere never intersected with the atmosphere.

If you cut off thrust at a point that is within the atmosphere then the resulting elliptical orbital path will intersect with the atmosphere. If you cut off the trust at the Earth's surface (e.g. with a launch gun) then the resulting orbital path will intersect with the Earth's surface.

As @Bandersnatch points out, you need a circularizing burn somewhere outside the atmosphere to change from the original elliptical orbit that intersects with the atmosphere to a more nearly circular orbit that does not.

 

[Bandersnatch]

Ta, @jbriggs444 .
In visual terms, this is what happens when you launch objects in a central gravitational field, with only the initial velocity:

Notice, how the projectile always returns (when it's in a bound orbit) to the launch point.

 

[Toaster]

Ok guys this thread is already a little complex, but let's simplify on the calculations from point A Earth's surface to point B in orbit (Imagine that once there, the capsule will be towed and stored on a safe place on our imagination :).

Temperatures are my nightmare right now, if you want to help me with that I will very much appreciate it.

 

[jbriggs444]

Ok guys this thread is already a little complex, but let's simplify on the calculations from point A Earth's surface to point B in orbit (Imagine that once there, the capsule will be towed and stored on a safe place on our imagination :).

So the question becomes: "how high does an orbit have to be to count as an orbit"?

You tell us. If I toss a baseball from center field to home plate, does that count as being in orbit?

 

[Toaster]

35000 meters could be the altitude needed to get towed
http://www.altitude.org/air_pressure.php

 

[Toaster]

As @Bandersnatch points out, you need a circularizing burn somewhere outside the atmosphere to change from the original elliptical orbit that intersects with the atmosphere to a more nearly circular orbit that does not.

It seems like a good idea, and we can modify the capsule's trajectory. But finding these data is where I get lost.

 

[jbriggs444]

It seems like a good idea, and we can modify the capsule's trajectory. But finding these data is where I get lost.

Orbital mechanics is easy. Aerodynamics is hard.

 

[mfb]

Do you know about the StarTram and Space gun concepts? ICBMs could also be of interest due to their high speeds at low altitude. If you follow the references there, you'll see that a lot of work got done already. Yes, you can shoot something through the atmosphere at orbital speeds at 4+ km height, heating is an issue but manageable.