“Continuous” would be more accurate than “constant”. It’s common that the force exerted by the rocket is more or less constant (while fuel remains), so the decreasing mass (due to fuel expended) leads to increasing acceleration.
Also on your distance from its center. For two planets of equal mass, escape velocity measured at the surface will be greater on the planet with greater density (and thus a smaller radius).
Thanks for all the come back, I have read and digested.
(Thought I did not too bad for a travel writer with an English degree!)
In one of the Hitchhikers books Douglas Adams writes that the secret to flying is to throw yourself at the ground and miss. It took me a while to realize that this isn’t just a joke, but actually quite a good description of how to get yourself into orbit!
*The Hitch Hiker’s Guide to the Galaxy has this to say on the subject of flying.
There is an art, it says, or rather a knack to flying.
The knack lies in learning how to throw yourself at the ground and miss.
Pick a nice day, it suggests, and try it.
The first part is easy.
All it requires is simply the ability to throw yourself forward with all your weight, and the willingness not to mind that it’s going to hurt.
That is, it’s going to hurt if you fail to miss the ground.
Most people fail to miss the ground, and if they are really trying properly, the likelihood is that they will fail to miss it fairly hard.
Clearly, it’s the second point, the missing, which presents the difficulties.
…
This is a moment for superb and delicate concentration.
Bob and float, float and bob.
Ignore all considerations of your own weight and simply let yourself waft higher.
Do not listen to what anybody says to you at this point because they are unlikely to say anything helpful.
They are most likely to say something along the lines of, “Good God, you can’t possibly be flying!”
It is vitally important not to believe them or they will suddenly be right.
Waft higher and higher.
Try a few swoops, gentle ones at first, then drift above the treetops breathing regularly.
Do not wave at anybody.
When you have done this a few times you will find the moment of distraction rapidly becomes easier and easier to achieve.
You will then learn all sorts of things about how to control your flight, your speed, your manoeuvrability, and the trick usually lies in not thinking too hard about whatever you want to do, but just allowing it to happen as if it was going to anyway.
You will also learn how to land properly, which is something you will almost certainly cock up, and cock up badly, on your first attempt.* [right]-- Douglas Adams, Life, The Universe, And Everything[/right]
This is actually a surprisingly accurate description of most ballistic and space launch rocket development programs.
Stranger
Would that all English majors did as well.
AH!! Now, that’s a most enlightening answer! Thanks!
So, one way of imagining how escape velocity depends on height is to imagine instead a rocket that begins in space, very slowly drifting directly towards Earth until it is dragged in, faster and faster, by gravity. And stipulate there are no aerodynamic losses. Except for the issue of the slight drift velocity at the start, and neglecting the Earth’s rotation, the falling velocity at any height is the same as the escape velocity there.
I imagined that the rocket is way up there during liftoff when the last burn ends - beyond the substantial part of the atmosphere, where the sky is black, etc etc - and think of how much faster the imaginary falling rocket would be at ground level than it would be way up there. The difference blows away what skydiving would feel like without air resistance. Seems like the burn portion of the trip out is a big chunk. But that perspective is way, way wrong; the atmosphere is a thin little skin, and being on top of it is peanuts in the grand scheme. Rocketry is perhaps more like gunfire than not, for the sake of optimization.
To be precise, the atmosphere provides a lot of resistance, so while Chronos is correct in saying that (in absence of drag) you want to achieve the required momentum as soon as possible to avoid wasting propellant that is used just to haul other unburnt propellant to altitude, the reality is that you can only go so fast in atmosphere without running into problems with drag, heating, aerodynamic loading, et cetera. The point at which maximum aerodynamic loading occurs during ascent is called max-Q alpha, and this is almost always where the the minimum structural line load margins occur. Max heating, being cumulative, tends to occur later in burn and is still significant in the upper atmosphere at high Mach numbers even though the aerodynamic loading is insignificant (a few pounds or less per square foot). So while you’d ideally like to enter into a ballistic track as soon as possible and use the minimum amount of fuel, other factors dictate just how fast you can stand to go, and with a manned vehicle or one with a delicate payload like a telecommunications satellite, there is a maximum axial acceleration and thrust oscillations that can also be tolerated which limits your allowable impulse.
Stranger