Radiation belt transit times

to GEO and the Moon

LibreOffice spreadsheet here

Excel/97 version here. Not sure about whether this will work with your version of Excel, this is the translation made by LibreOffice, and I don't have any computers that run any of the myriad versions of Windoze or Excel.

LibreOffice is available for free download here.

I used the equations here on the server sky website.

• 1 from the altitudes and Earth's equatorial radius, compute radii
  • assume all orbits are circular equatorial. Inclined orbits require an expensive plane change, best done after circularization
• 2 Given apogee and perigee and the Earth gravitational parameter, compute
  • Semimajor axis
  • Eccentricity
  • Orbit angular velocity
• 3 Given the radius of the lower and upper bounds of the inner belt (altitudes 200 and 1000 km), compute
  • true anomaly angle
  • eccentric anomaly angle
  • mean anomaly angle
• 4 from the difference in the mean anomaly angles and the orbital angular velocity, compute transit time

Conclusion: an transfer orbit from ISS altitude to GEO takes 21.8 minutes to pass through the inner van Allen belt, and 18.2 minutes to pass through on the way to the Moon.