Is it reasonably possible to construct a cannon which can launch
objects (on the order of 10's of grams) _purely ballistically_ to the
moon?


Yep, this is another question resulting from a silly conversation that
led to a bet.  You guys did so well last time
(http://answers.google.com/answers/threadview?id=341982) I was hoping
you could do it again :)

As you can tell from the "reasonably possible", this question is
fairly open to interpretation.  Feel free to explore it from whatever
angle seems suitable to you to arrive at "what is necessary" for this
to be possible ... and then make your own opinion of whether this is
"reasonable" (not from a coporate sense, but maybe that of an
extremely dedicated amateur).
  
So here's roughly the backdrop,
- a bullet leaving a gun has a velocity on the order of 1 km/sec
- the escape velocity of earth is roughly 11 km/sec

the conversation then degenerated to a long series of assumptions and
hand waving over whether this means a ballistic shot to the moon is
possible for small objects.  We tried to find a way to estimate the
drag on such an object due to air (which would make the "true" escape
velocity much larger), and also find a way to estimate what speed a
projectile could be accelerated to in a cannon, given x amount of
explosive y.  Then look at the cost of such a thing to decide if it's
"reasonable" for an obsessed hobbyist.  If you feel this isn't the
best way to approach the problem, feel free to create a new route.

Thanks in advance!

P.S. For the purely curious who are wondering, this conversation was
sparked by a chance encounter with a crazy guy who claimed as a young
lad, had built such a cannon that shot lead slugs to the moon.  None
of us believed him, but when someone pointed out that a bullet was
only an order of magnitude away from the escape velocity ... we
started wondering if some crazied hobbyist could actually accomplish
such a feat.

An extra prize of $10 will be given if you can find an instance of
someone actually accomplishing this, as long as it describes how in
the world they did it.

Thanks again...

Snesprogrammer

Thank you for an interesting problem.

YES. It is possible. It is however very hard and so
'an extra prize of $10'  is unlikely to be claimed.

The question is not fully defined:

 What exactly is a cannon,
 what is the maximum allowed length of the barrel and
 what maximum acceleration is allowed
  
  may tip the answer to no.
 
 Conventional definition:

A large mounted weapon that fires heavy projectiles. Cannon include
guns, howitzers, and mortars.
http://dictionary.reference.com/search?q=cannon

and requiring use of explosive to deliver the kinetic energy may be to restrictive.
As mongolia-ga pointed out, acceleration generated during conventional
firing would be enormous.
  
  However, by ballistic launch we may consider any launch in which
kinetic energy was delivered before
  the projectile separates, so that no propellant needs to be 
expended after the separation.

  

  Since  as you say

 "Feel free to explore"
 
 I will consider a mass driver as an ballistic launch device. As we
will see below, NASA studies of the concept
 specifically recall Jules Verne's concept as a forerunner of this
method. The fact that while is was not build yet,
 it was a subject of serious studies by serious people, can be taken
as an evidence that such device is
 'reasonably possible'.
 
 Here are the details:

The use of mass drivers to throw 200 pound blocks of aluminum in to
orbit around the Moon came from Gerald O'Neal
in the 1970 ties. O Neal, a Princeton physicist was exploring
economical ways of building habitat in Space ( L5 colony) :
http://www.space-where-i-want-to-be.120host.net/sagan.html

The Earth's strong gravity and thick atmosphere make such an
installation difficult, so many proposals have been put forward to
place such an installation on the Moon.
http://en.wikipedia.org/wiki/Mass_driver

Mass Driver for Escape Velocity 

A proposed plan for the mass driver is shown above. 
The track is 100 kilometers long and slopes gently upwards. The
payload capsule has a mass of

http://www.phy.duke.edu/~rgb/Class/review53/node80.html
http://www.asi.org/adb/02/10/mass-driver-aiming.html


Serious paper and software for design of Earth based mass driver
http://deed.megan.ryerson.ca/~fil/I/Papers/iaf2004.pdf

FINALLY:

GLTS - NASA system
GUN LAUNCH TO SPACE (GLTS)MASS DRIVER LAUNCH SYSTEM -- JULES VERNE LAUNCH SYSTEM)
has drawing of such system:

After the shell reached 2.7 miles per second (end of gun), the
projectile would have sufficient velocity to pass through the Earth's
atmosphere. The acceleration of one thousand to two thousand G's would
require acceleration hardened payloads. The armature would separate
and fall to Earth. The aeroshell would also drop away, and the rocket
motor would add a delta v of 2.7 miles per second to reach orbit.

http://vesuvius.jsc.nasa.gov/er/seh/know23.html

Furthermore,
  
  If we do not place a limit on the 'length of the barrel' then answer
is certainly  'yes' .
  We consider a driver / space elevator hybrid. We can imagine a
combination of space elevator with
  linear motor, which will release the projectile at high altitude,
where air resistance is less of a problem.
  
   But, even without 'stretching out' the concept of the cannon this
much, then answer is - yes, the concept is
   reasonably possible.
     
   
   Hedgie

---

Clarification of Answer by hedgie-ga on 27 Dec 2004 00:44 PST

Thank you for the rating.

 It is an interesting question, and I got quite intriqued by it.

 In the end, I was answering question ' is it physically possible'?
 rather then question as you posed it. 

 I agree that answer to 'can obsessed hobbyist do it' is NO.

 Of course, notion of' hobbyist' is somewhat undefined. The guy in
'The incredibles'
http://www.imdb.com/title/tt0317705/
probably could do it. But he is an fictional character, isn't he?

PS. I see 'electromagnetic rail gun' as a special case of a mass driver.
     In general case one can eliminate electric contacts (and arcing) and
     use induction and maglev ..

Hedgie

Thanks for all the information.  It's quite interesting. 
Unfortunately, after reading through the links, I've come to the
opposite conclusion as you: No, this is not possible for an extremely
dedicated hobbyist.

Most links talk pure hypothetics, which is useful to help me
understand how such a device would work.  Then this link:
http://deed.megan.ryerson.ca/~fil/I/Papers/iaf2004.pdf
talks a bit about the current technological limits, including "The
launch velocity of a conventional powder gun is limited to 3 - 4
km/s;"  It doesn't really explain why, but at least we can see that an
"explosive" cannon type device isn't really going to work.  Then
looking at "Table 1: Present Launcher Technology Performance" we can
see the limits of some selected projects (up to year 2003).  None are
capable of reaching escape velocity for something on the order of tens
of grams. (The HARP project that andy2205-ga mentioned in the comments
is listed in that table as well.)

I've read through the wiki link and followed links from there as well,
and must admit I still don't fully understand how a mass driver
differs from a rail gun ... so I still have reading to do :)  But some
links led to reports of current research and it looks like even with
government backing through grants, such launches are not yet possible.

So I'll have to say No to the crazed hobbist. (Feel free to correct me
if I'm missing something important here.)

I gave you a 5 star rating because the info was quite interesting, and
you did _great_ in taking liberties to explore new ideas (I never
considered electromagnetic propulsion schemes when thinking about this
previously).  Thanks :)

Dear Snesprogrammer

I am indeed intrigued by the possibility you suggest. You are probably
aware that this was the mechanism that Jules Verne suggested for
sending men to the moon in his Science Fiction book 'From Earth to
Moon' In the story the actual space capsule was a large 'bullet'
launced from a cannon. As with so many Science fiction stories it
ignored a few minor technical details such as the fact that the g
forces created in the first second of launch would reduce any human
being to a pure mush.
I also understand (and this is something that Google Researers may
want to investigate), that the US government may have launced a number
of very low
mass objects into orbit sometime in the late 1950's using the technique you
suggest.

 However to send something to the moon using this method that is
something I am not qualified to answer and I will leave it to our
learned friends in the Google Researcher community to answer your
interesting query.
Yours Truly
Mongolia

You may want to check out the "Harp" project which the defence
department used a cannon to shoot projectiles up to altitudes of
>90,000 feet (I think) this is far short of reaching the moon of
course.

"Early BRL experiments with dart-shaped vehicles capable of ejecting
radar reflective chaff at high altitudes proved successful. This led
to the development of the BRL 5-inch gun system capable of lofting a
26 lb. sub-calibre gun probe to an altitude of 50 miles. This gun
system was used extensively during HARP (300 flights) for atmospheric
research and was the foundation for all future HARP gun systems."

http://www.astronautix.com/articles/abroject.htm

My first thought was "Purely ballistic projectal to the Moon is
impossible, by ametures" I'm still wondering if HAARP achievements may
be government propaganda = disinformation. Antiaircraft guns reach a
heigth of about 12 miles, only 1/4 million miles to go. Single stage
rockets (not pure balistic) reach heights of about 200 miles. S = 1/2
at squared = 1/2 10 times 2 billion = 10,000,000,000 feet = 189,000
miles. (That is an average of about 1/3 g over this part of the trip
lasting 100,000 seconds = 27.777 hours) The projectal would fall the
rest of the way to the moon. Earth's gravity decellerates the
projectal for almost 200,000 miles of a ballistic trip to the moon.
 A cannon with the muzzle 50 miles above sealevel might reach the
moon. The muzzle velosity would need to be about 20,000 MPH = 5.5555
miles per second = 29,3333 feet per second. At lower altitudes, air
friction would vaporize the projectile, if that high muzzle velosity
is achievable with known materials, and extremely long barrel. Air
friction losses are very high this fast, so much greater muzzle
velocity would be needed.   Neil

oops! Bad arithmetic, 100,000 seconds is too long, 1/3 g may be more
than the average. 44,721 seconds is the square root of 2 billion. That
is 12 hours to the 189,000 mile point. Advanced calculus would give a
slightly different answers.   Neil