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Sattelites beyond Jupiter - problem setup

  1. Dec 6, 2008 #1
    1. 1. Analytical With the help of `Maths27', formulate the problem of when to launch the
    satellite, based upon the radii of the orbits of Earth and Jupiter, assuming that both
    planets have circular orbits and ignoring all potentials except that of the sun.
    Provide the equations of motion for the satellite under the assumptions that; the mass
    of the satellite is negligible in comparison to planetary masses, the Earth's gravitational
    field may be neglected and that all motion is coplanar.

    Should you launch the satellite in phase with the Earth's orbit or opposed to it?

    2. Numerical Using a Runge-Kutta algorithm (see `Maths20'), write a program to solve
    the two body problem for the satellite's motion from Earth to Jupiter. Assess your calculations
    using the exact analysis provided in `Maths27'. Now extend your calculation
    to incorporate Jupiter's gravitational potential, paying special attention to real conservation
    laws for the chosen limit and approximate conservation laws which would be true
    in the absence of Jupiter. You will need to have an algorithm to provide an automatic
    step-length control: The use of two Runge-Kutta algorithms to assess the error is a very
    efficient method. Pay particular attention to picturing the answer.

    3. Investigation Devise a strategy for giving the satellite the biggest kick from Jupiter's
    gravitational potential. Does the satellite approach `dangerously close' to Jupiter? Can
    the satellite escape from the Solar system? Provide a simple argument to predict the maximum
    impulse from Jupiter, and the corresponding minimum planetary orbit to achieve
    escape from the solar system.

    4. Data
    Gravitational Constant 0:667 1010m3kg1s2
    Mass of the Sun = 0:1984 1031kg
    Mass of the Earth = 0:5976 1025kg
    Mass of Jupiter = 0:1903 1028kg
    Radius of the Earth's Orbit = 0:1495 1012m
    Radius of Jupiter's Orbit = 0:7778 1012m
    Radius of the Earth = 0:6368 107m
    Radius of Jupiter = 0:6985 108m



    I have C++ code for a fourth order runge kutta but am unable to set up the differential equations to solve this problem. Should I set up a space marix containing potential values and then update it as time procedes (planets move) and then map the motion of the sattelite in accordance with these values? Help with this would be greatly appreciated.

    Any links to resources onlnie resources would be very helpful as fruits from various google searches yielded little in the way of this problem.



    Thanks

    Sol
     
    Last edited: Dec 6, 2008
  2. jcsd
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