They are almost entirely unrelated. When trying to leave the gravity well of a planet, the atmosphere is only a dragging force acting to reduce your thrust. It might be proportional to the surface area of the vehicle, but likely not - I think it's only proportional to the surface area of the "nose" of the rocket. But what's certain is that it's strictly a force that hinders you - in a rocket, all of your thrust comes from the engines, you don't get any boost from the air.

However, even if you're taking off of a planet with no atmosphere, you still have a huge force to deal with - you need to maintain an acceleration to exit the gravity well of the planet, and you need to burn fuel for that. But you also have to carry the fuel you'll burn with you, so the more fuel you have, the more fuel you'll need - this is what the rocket equation codifies.

> But you also have to carry the fuel you'll burn with you, so the more fuel you have, the more fuel you'll need

Isn't this the entire point of using methane as fuel so that they can build a gas station once they get there so that return fuel is not required to be considered in this equation?

I'm not talking about fuel that you need to get back, we're still at the "leaving Earth" case. The point is that you need, say, 1000 tons of fuel to leave the Earth. Your rocket then will weigh [weight of empty rocket] + [weight of payload] + 1000 tons. And it is this mass that the engines will have to push while ascending. Of course, the fuel gets spent as you ascend - by the time you reach orbit, your rocket is now 1000 tons lighter.

ahh, I misread the part I quoted. doh!

The refueling idea is so that for example you don't need to carry the fuel needed to get to the moon or Mars all in one rocket. You just need to carry enough to get to the refueling orbit - which is much less.

>A little Estes toy rocket lifts off the pad much more aggressively (in the blink of an eye!) than a full size rocket...

If you really want to, you can reach Mach 10 (~3300 m/s) with a 8 meter long 3500 kg missile in 5 seconds:

https://en.wikipedia.org/wiki/Sprint_(missile)

All of that in the lower atmosphere with the missile heat shield glowing white hot. :)

Most of the aggressiveness of a toy rocket is the smaller length. Orbital class rockets are literally the size of skyscrapers.

The toys have to be aggressive. You have less than three feet worth of launch rail--by the time the rocket clears the rail it must be going fast enough that the fins make it stable. Meanwhile, it's light, overengineering the body to take a high g load is trivial.

An orbital class rocket--taking that kind of g load is going to break it (just look at the payload specs for the Falcon Heavy--its maximum permitted payload is well below it's performance to low orbit. You load it up to what the engines can do, it breaks. The only use case is when it's going farther than low orbit.) And an orbital class rocket has active steering rather than fins, it doesn't need to be booking it to be stable.