Thrust needed from an engine to reach orbit

Assume you had an airplane with magical engines that didn't need fuel, air or power, to operate. What thrust to ground weight ratio would the airplane need to reach orbit? By ground weight I mean mass times 9.81.

Assume not needing fuel, air or power is the only magical property of the engines and the aircraft is otherwise made from modern day technology.

Obviously a thrust to weight ratio greater than 1 would work, but I have a hard time reasoning what would be a realistic minimum.

Every time I think about it, it seems that if the airplane could lift off the ground it could reach orbit, but that doesn't seem right. My reasoning is that since both drag and lift are proportional to velocity squared (see here) as the airplane gets faster, it could just climb to a higher altitude and lower density to compensate. The airplane would just go faster and faster (and go higher and higher to keep a constant lift and constant drag) and eventually reach orbit.

• Drag is proportional to the square of velocity. A plane needs to be moving at orbital velocity to get lift beyond about 80 to100 km altitude (the Kármán line). And there's still a lot of air at 100 km altitude, at least so far as a fast moving object is concerned. A plane cannot make it into orbit. – David Hammen Mar 22 '19 at 23:53
• Just to be clear, given the stipulated magical engine, what precisely do you mean by "eventually reaching orbit"? – Alfred Centauri Mar 23 '19 at 0:05
• @David Lift is also proportional to the square of velocity. The aircraft would reach 100km before reaching orbital speed. I don't know what the exact trajectory would be, but as velocity slowly increases so would altitude, keeping both drag and lift constant. Maybe that is not possible, but I don't see why. – Andrew Mar 23 '19 at 8:48
• @AlfredCentauri By orbit I mean that if the engines were turned off it would stay in orbit. The specific orbit isn't important, but lets say the same orbit as the ISS. Initially the air would be responsible for 100% of the lift, but as the airplane gets closer to orbital speed (and higher in altitude) the "effective weight" (sorry I don't know the right term) would be less, until at orbital speed the "effective weight" would be zero and no more air would be needed for lift. – Andrew Mar 23 '19 at 8:54
• I think you're right. One reason airplanes go to high altitude is so they can go faster because the air is thinner. But they have a problem - thinner air = less thrust. If your magical engines keep their thrust then they can just keep accelerating, up to orbital speed and beyond. By the way, don't look at thrust vs. weight. Look at thrust vs. MASS. – Mike Dunlavey Mar 24 '19 at 22:50