(a) Suppose a projectile is launched vertically from the surface r = R of the earth with...
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(a) Suppose a projectile is launched vertically from the surface r = R of the earth with initial velocity v0 = √2GM/R, so v20 = k2/R where k2 = 2GM. Solve the differential equation dr/dt = k/√r (from Eq. (23) in this section) explicitly to deduce that r(t) → ∞ as t → ∞.
(b) If the projectile is launched vertically with initial velocity v0 > √2GM/R, deduce that
Why does it again follow that r(t) → ∞ as t → ∞?
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Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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