Solving equations numerically in Mathcad 2001i Professional

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SUMMARY

Henrik seeks to calculate a spacecraft's trajectory from Earth to the Moon using Mathcad 2001i Professional, specifically addressing a two-dimensional problem outlined in a referenced PDF. He successfully solved a one-dimensional scenario but struggles with incorporating the slingshot effect around the Moon. The discussion highlights the importance of using initial x, y coordinates and velocities to compute acceleration iteratively, suggesting a numerical approach to solving the equations of motion.

PREREQUISITES
  • Understanding of orbital mechanics and slingshot maneuvers
  • Familiarity with Mathcad 2001i Professional
  • Knowledge of numerical methods for solving differential equations
  • Basic concepts of two-dimensional motion and vector calculations
NEXT STEPS
  • Research numerical integration techniques for trajectory calculations
  • Learn how to implement the "for" function in Mathcad 2001i Professional
  • Study the equations of motion in two dimensions for spacecraft navigation
  • Explore examples of slingshot maneuvers in astrodynamics
USEFUL FOR

Aerospace engineers, physics students, and anyone interested in spacecraft trajectory calculations using Mathcad.

Henriklm
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Homework Statement



Hey there..

I would like to make a path for a spacecraft from Earth to moon, and back again. I found this pdf that explains how, but i can't figure it out.

Homework Equations



http://courses.ncssm.edu/math/NCSSM%...r%203/Moon.pdf

"Part II: The slingshot around the Moon. A two-dimensional problem" (p. 4-6).

The Attempt at a Solution

Is the trick to take initiating x,y coordinates and x,y velocity, calculate the acceleration at that point and then calculate where it will be after 0.001 t, then calculate the new acceleration and velocity and so on?

How can I solve this using Mathcad 2001i Professional?

Or am I approaching this the wrong way?
I´ve solved the first part of the PDF, where it is in one dimension, but I can't figure out how to do it in two dimentions :S

Thank you :-)

Henrik
 
Last edited by a moderator:
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I'm not sure how to use the "for" function, but here goes

http://img819.imageshack.us/img819/6548/billedtilsp.jpg

mmåne = mass of moon
mjord = mass of earth
xmåne = x position of moon
ymåne = y position of moon

Earth = (0;0)

Could this be a solution? Am i going down the right path, or is it a dead end this way. If not, what could be a solution?

Thank you :-)

Henrik

P.S. I am sure there is a lot of errors in the equation for acceleration, but I can always fix that later :-)
 
Last edited by a moderator:

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