QUESTION: Is it practically possible that a rocket/spaceship maintains a constant speed (say 10 km/hr) and still manages to escape the Earth's gravitation field???
Please Elaborate quantitatively and Qualitatively too!!
ANSWER: Yes, a rocket can escape the Earth’s gravitational field at a constant speed. But first it must achieve the minimum orbital speed given by:
vo = sqrt(GM/r) = ve/sqrt(2), where
vo = orbital speed, G = gravitational constant, M = mass of Earth, r = distance between mass centers, and ve = ballistic escape velocity (11.2 km/s on Earth).
Then to escape the Earth’s gravity well, the speed must increase such that the characteristic energy, C, in the following equation is greater than or equal to zero:
C/2 = 1/2 * v^2 - mu/r, where
mu = GM
Since your rocket speed of 10 km/h is much less than the ballistic escape velocity, it would not be able to go into orbit nor escape the gravity well.
---------- FOLLOW-UP ----------
QUESTION: Basically is this what you are trying to say:
"The rocket needs to maintain the minimum orbital speed throughout..??"
What i was asking is this:
Suppose i counter the gravitational force and then due to zero acceleration,
the speed becomes constant..
so at this speed the rocket must escape the earth..
Is this Practically possible????
I'm not sure I understand your question. The rocket must attain the necessary speed as a function of altitude described in the above equations. To get to that speed the rocket must accelerate. Once it achieves the necessary speed it can remain at that speed forever (or change speed as the gravitational field diminishes with altitude).