Radiation belt transit times to GEO and the Moon

LibreOffice spreadsheet here

Excel/97 version here. Not sure 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.

I assume all source and destination orbits are circular equatorial. Inclined orbits require expensive plane changes after circularization. I assume the lower orbit is approximately at ISS altitude, but not at the steep inclination of ISS.

The Moon's inclination is actually 5.145° to the ecliptic, and the Earth's axis is tilted 23.4392811° to the ecliptic, so the plane change from can be as much as 28.6° and as low as 18.3° depending on where it is in its 18.6 year precession cycle. None of these inclination details affect the transit time through the van Allen belt, though they (and launch site latitude) do greatly increase the complexity and delta V cost of a mission.

• 1 - from the altitudes and Earth's equatorial radius, compute radii
• 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: a Hohmann 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 the inner belt on the way to the Moon.