Now, I wonder if an air-launched spacecraft in the next 20 years realistically could really fly us to the moon - that is, could they reach escape velocities?
Air launch to LEO: Done now
Air launch to lunar orbit - yes, but at 20%-25% of LEO payload
Air launch to Moon and back to LEO: Yes, but with about 5% of LEO payload
It is easy to overlook some practical realities when enthusing over paper-based systems.
Ratio of air-launched vehicle mass to winged return-to-base Mothership mass must not be overlooked. The Mothership size sets an upper limit to the space-vehicle mass. Increases above heavy lift aircraft payload masses may be possible with eg balloons, but this calls for some extremely specialised systems. Looking at the figures below it looks like manned lunar return to earth's surface is an unrealistically high expectation for air launched systems. Small unmanned craft to lunar orbit are practical.
The answer is "yes, obviously" as you can build a small-er lunar launcher than is usually used and you can conceivably build a means to air-launch it. eg Balloon launch can allow very substantial mass and has been proposed in various studies.
The existence proof of the general concept comes in the form of the several "Orbital Sciences Corporation" air launched orbital vehicles. These are only used for LEO (low earth orbit) insertion but escape velocity would be achievable given a suitably small payload.
The material below gives examples of what could be realistically achieved based on existing small air-launched LEO satellite launchers and the as it was then 2013 proposal from Orbital Sciences, Burt Rutan and Paul Allen.
This demonstrates that a not insignificant air launch could deliver about 800 to 1000 pounds to lunar orbit - more with utter leading edge fuels and systems or even larger 'motherships'. This is uncomfortably smaller than what you realistically want to deliver one person to lunar orbit and back. While scaling is possible it's not looking attractive for multi-person lunar return flights.
The advantages of aerial launch is not altitude gain as such but the significant gain in reduced air resistance, and the small gain in velocity. While the air launch velocity is a minor fraction of orbital velocity, a ground based launcher must add the initial velocity while supporting the maximum mass against gravity. This is minor compared to air resistance losses, but useful. Air resistance halves about every 15,000 feet, and drag is inversely related to air density. And drag is proportional to velocity squared - so if you can start slower and higher it can help significantly. You will ultimately need very substantial "horizontal" velocity to orbit, but initially, getting up out of the thick lower atmosphere with minimal losses is extremely important. The "mothership" has wings and air breathing engines and fuel is cheap compared to the cost of carrying it to high altitude and high velocities, so an air launched system provides gains in launch vehicle costs and capabilities in situations where it is reasonably possible to build a large enough "mothership". For small LEO payloads it's eminently viable (and used), for very small one way lunar payloads its doable, but for lunar return, the mothership logistics start to become formidable.
Here is a video of the air launch of an XL Systems "Pegasus". This shows the action from just before launch until stage 1 burnout.
The "next stage" of this capability as of May 2013 is shown here.
Stratolaunch and Orbital – The Height of Air Launch . How this has been modified by more recent events I know not but this showed what was being planned in 2013 so is pertinent to your question.
This launcher proposed a 13,500 pound payload to LEO.
That's not vast - but definitely provides useful payload
The assignment of relative delta V's and fuel requirements to missions is too complex to allow simplistic answers that cover more than specific examples, but as a really really rough indication, the "delta-V" from LEO to lunar orbit is very approximately 40% of that required to reach LEO from the earth's surface. The table below provides velocity changes needed for various orbital and location transitions. This gives 3.9 km/s as the delta V needed from LEO to lunar orbit.
The basic formula for calculating velocity change for a rocket is the (not surprisngly) "rocket equation: -
Call M2/M1 = mass ratio = MR.
Using a modest by modern standards Isp of 300, to produce a delta-V of say 4000 m/S requires a MR of about 3.7 or end mass ~= 1/3.7 = 27% of total.
So ABOUT 25% of the above 13,500 pounds could be delivered to lunar orbit
=~ 3375 pounds = 1.5 tons
~= 1.5 tonnes :-)
This in turn could return about 840 pounds to LEO and a rather lesser amount back to earth. The table below is from this Delft university page
Pegasus launcher pictures with links
OSC Pegasus - 44 launches since 1990.
Pegasus XL - 443 kg to LEO so ABOUT 100 kg to lunar orbit.
NASA Pegasus mission 2014
OSC Facebook page
Inner system delta V chart
From **Wikipedia - Delta-v budget
and also used in this stack exchange post