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Rocket Equation with varying gravity

  1. Aug 6, 2009 #1
    So, the rocket equation is

    F_ext = m(dv/dt) + u(dm/dt)

    where m is the mass of the rocket, v the velocity, u the effective exhaust gases speed, and F_ext the external forces on the system.

    If we take a constant mass ejection rate p, and take the external force to be the gravitational attraction of a mass M, we recover the differential equation

    (d^2x/dt^2) + GMx^(-2) = up/(m0 - pt)

    where m0 is the initial mass (time t=0).

    Can this type of differential equation be solved analytically? If so, how would one go about it?


  2. jcsd
  3. Aug 6, 2009 #2


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    Science Advisor

    Almost positive it's not solvable analytically, seeing as it's 2nd order non-linear. A quick run through mathematica seems to support that.
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