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| '''Conclusion:''' a 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. | '''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. |
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: 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.