- #1
RiotRick
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- 0
Homework Statement
In the far future, humans have built a space elevator as a cheap
means of access to space. However before that could be done, a few basic principles had to be
worked out. . .
a)
What is the minimum initial speed (in an Earth-centered inertial reference frame) needed
for an object launching from the Earth surface (r = rE) to escape its gravitational influence
entirely? You can rely on conservation of energy.
b)
Objects can be launched into space from the elevator “just” by moving them up the elevator,
until a certain height, and then releasing them (with zero radial velocity). What is the
height ##r_{esc}## (as measured from the centre of the Earth) the elevator needs to have so that
the released object would ultimately escape the Earth’s gravitational influence? Careful:
the escape speed has not the same value as for the previous question.
Homework Equations
The previous question asked for the initial escape velocity.
##F_G = G*\frac{M*m}{r^2}##
The Attempt at a Solution
a) is solved via conservation of energy
b) Here I don't fully understand the question. The "careful" makes me suspicious. Do I set centrifugal force equal to the gravitational force or does it ask for the tangential velocity? So I'd have to set the tangential velocity equal to the escape velocity
##\omega*r=\sqrt(\frac{2GM}{r})##