Reaching orbit is mostly an issue of velocity, not altitude. This is why balloons can get very high, above of almost all earth's atmosphere, while being far from orbit. Rockets spend most of their ascent traveling nearly horizontal to the ground (they only go straight up at the beginning to get out of the densest part of the atmosphere).

Exactly. The most expensive part of getting to orbit is circularization. It takes a delta-vee of ~9.4km/s to reach LEO from earth. If you could lift yourself into LEO altitude without any thrust, you'd still have to circularize to the orbital velocity of ~8km/s [!]. That's still the majority of your delta-vee!

[!] I am not a rocket scientist, so I haven't taken into account the orbital velocity you'd get from being rooted on the earth at takeoff, but it should be at most ~500m/s.

The train would glide the aircraft to the mesosphere (50 km or 31 miles) and than rocket to orbit? So you would need 62+ miles of track going hundreds of miles an hour at 45 degree angle with the tow rope?

What about geostationary orbit wrt balloons? Do the balloons slow down horizontally a lot during the ascent? If not, what if we floated a rocket up most of the way and let the rocket do the rest?

Balloons float because dense air in the lower parts of atmosphere pushes them up with buoyant force. They lose the ability to float way before they would reach LEO, let alone GEO.

You've just described a ballocket. You launch a rocket from a very high altitude balloon.

You gain nothing from the height, because you still need to spend ~10km/s getting up to orbital velocity, but you don't have to push your way through the thick lower atmosphere any more. Rockets don't work very well in atmosphere, so you do get fuel savings due to more efficient engines.

I don't know if this has ever been tried for real.

Rockoon? https://en.wikipedia.org/wiki/Rockoon I particularly like the steampunk vibe of https://en.wikipedia.org/wiki/JP_Aerospace#Airship_to_Orbit_...

Er. * cough * Yes, rockoon, not ballocket.

In my defence I (a) am coming down with a horrible cold, and (b) read The Register...