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The Effects of a Radial Impulse

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Newbie

The Effects of a Radial Impulse

By Roger Mansfield

Maneuvering a Spacecraft Orbiting the Earth

07_feb-orbitalimpulse.png

About this worksheet:

  • Solves the question, "In what direction would a spacecraft move if you fire a pulse purely along the radius vector and perpendicular to the instantaneous velocity vector, assuming circular orbit?" 
  • Applicable in aerospace, math and statistics, and physics 
  • Performs state vectors, orbital elements, apogee and perigee, velocity vector magnitude, flight path angle, angular momentum vector magnitude, Hohmann transfer, etc

This worksheet attempts to solve a problem that asks what direction a spacecraft would move in if it fired a pulse purely along the radius vector and perpendicular to the instantaneous velocity vector, assuming circular orbit. To answer this question the worksheet first defines some of the constants and conventions including: 

  • Number of degrees in one radian 
  • Gaussian constant for earth relative motion 
  • The secondary's mass is negligible relative to earths mass 
  • Earths mean equatorial radius in km 
  • Origin 
  • A conversion from E.R./kemin to km/sec

Using PTC Mathcad, the worksheet shows you how to construct a state vector (position and velocity) for the geostationary orbital radius and transform it to orbital elements. You are also shown how to add the outward, radial impulse to the velocity vector and transform this second state vector to orbital elements.

This worksheet is complete with background information, step by step instruction, all data and formulas, along with solutions and graphs to prove the solution.

Download and explore this worksheet yourself! You can download a free lifetime copy of PTC Mathcad Express and get 30 days of full functionality.

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