Your mostly correct , but there are issues that need picking.
ie...
In general your summary is correct. I have a
few comments. Generally the definition of 'escape velocity' is
the required unaccelerated initial speed required to escape
into space and not return.
escape velocity would send the vehicle away from the earth
and at the same time once the vehicle stopped accelerating
away from the earth the vehicle would then begin to gradually
decelerate due to the gravitational attraction between the
vehicle and the earth until the vehicle comes to a stop
and at that time the vehicle would begin to accelerate towards
the earth or towards the largest gravitation field that it
is attracted to.
For your second point you can generalize it to
say 'any force greater than the mass of the vehicle'.
true , because the mass is only 1 kilogram on the earth , so
in generalizing it you are correct as the any force
above 1 kilogram force would not stand correct on a planet
with a stronger or a weaker gravitational field.
For your third point I'm not sure exactly
what the value would be.
the constant verticle acceleration of the vehicle
with a force greater than the mass of the vehicle would
give the vehicle constant acceleration , there is no
exact value here as any value of force can always be lowered which
in turn lenghtens the time required to lift off.
Your 4th item is a little trickier. My feeling is that
you are approximately correct. Again this depends on a constant
acceleration drive, which doesn't expend mass from the vehicle.
That is the problem with today's space vehicles. We have to expend
huge amounts of energy to achieve the acceleration required to get
to space. But we have to start with full fuel tanks, and that fuel
has to be accelerated too. Most of the fuel used to launch a space
vehicle is used just to lift the fuel.
all true except the approximately correct part because I did
include in the specs that the vehicle supplies its own propulsion
and the vehicle has a mass of 1 kilogram.
but I should have also noted that the vehicle does not throw mass
away from the vehicle in order to achieve propulsion.
and with the common laymans type of rocket propulsion systems
that are still currently used I can understand how it would be
easy to think that my answer might be incorrect even though it
was not.
As far as a purely vertical takeoff is concerned we don't do it
because the real world doesn't work according to our simplified models
and we have to work with what we have.
a more correct statement would be that we dont do it because of the tools
that we are allowed to use to accomplish a goal due to economic and political
reasons.
