- #1
RubinLicht
- 132
- 8
Homework Statement
solve for escape velocity from Earth's surface
Homework Equations
just either use the line integral, and the tangential term disappears, or just use the energy equations
The Attempt at a Solution
I've solved it, but I'm having some trouble just coming to grips with this.
in terms of motion, isn't it possible to have circular motion around the Earth at any radius? so, if you launch at some arbitrary angle from the earth, could there be an angle that you launch at where the mass ends up more in an orbit rather than escaping Earth's gravitational field? (or maybe the total energy associated with circular motion is less than escape velocity, in which case I guess this is not possible, I'll work this out in a bit)
now that I think about it, if you solve the conservation of energy equation, isn't there an implicit assumption that the mass will take the path such that it ends up at an infinite distance from earth? is this a valid assumption? does energy guarantee that a particle will take a path that arrives at "infinite" radius? I thought it only guaranteed that there's enough energy to reach that state, but it might not necessarily ever get there?
please ask for clarification if my reasoning is hazy