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== Characteristics of typical radiation belt charged particles ==

The following table appears in [1][2][3] .  The gyration numbers seem to be '''incorrect''' for the 500km altitude.
Depending on the magnetic latitude and pitch angle of these "typical particles", 
the table values for the gyration period are between 2.3 and 5.0 too large, 
as if the B field is 3x too small or the altitude is 2800 km instead of 500km .
This does not even occur over the south Atlantic anomaly, which brings the lower
field down only 500km or so.

||<|3>                                                  ||||      Particle     ||
||                                                         1 MeV    || 10 MeV  ||
||                                                         electron || proton  ||
|| Range in aluminium (mm)                              || 2        || 0.4     ||
|| Peak equatorial omni-directional flux (cm^-2^ s^-1^) || 4E6      || 3.4E5   ||
|| Radial location (L) of peak flux (Earth-radii)       || 4.4      ||  1.7    ||
||<-3> Radius of gyration (km)                                                 ||
||     500 km                                           || 0.6      || 50      ||
||     20000 km                                         || 10       || 880     ||
||<-3> Gyration period (s)                                                     ||
||     500 km                                           || 1E-5     || 7E-3    ||
||     20000 km                                         || 2E-4     || 0.13    ||
||<-3> Bounce period (s)                                                       ||
||     500 km                                           || 0.1      || 0.65    ||
||     20000 km                                         || 0.3      || 1.7     ||
||<-3> Longitudinal drift period (min)                                         ||
||     500 km                                           || 10       || 3       ||
||     20000 km                                         || 3.5      || 1.1     ||

Constants:

|| Magnetic field constant || Tesla   || 3.0037E-05 || B,,0,, ||
|| Unit charge             || Colombs || 1.6021E-19 || q      ||
|| Joules per MeV          || J/MeV   || 1.6021E-13 ||
|| Earth radius            || m       || 6378210.00 || R,,E,, ||
|| Speed of Light          || m/s     || 2.9979E+08 || c      ||

Let's compute some numbers at 500km altitude:

|| ratio                            ||       |||| 1.078               || ratio = 1 + alt/R,,E,,      ||
|| L @  0 degrees magnetic latitude ||       |||| 1.078               || L=ratio                     ||
|| L @ 90 degrees magnetic latitude ||       |||| infinite            ||
|| B @  0 degrees magnetic latitude || Tesla |||| 2.40E-05            || B,,lat0,,=B,,0,,/ratio^3^ . . . ''* sqrt( 4-3 ratio/L )'' ||
|| B @ 90 degrees magnetic latitude || Tesla |||| 4.79E-05            || B,,lat90,,=2B,,0,,/ratio^3^ . . . ''* sqrt( 4-3 ratio/inf )'' ||
||||<|2>                                  ||||        Particle        ||
||                                           electron   || proton     ||
|| Kinetic Energy               || MeV    || 1          || 10         ||
|| Kinetic Energy               || J      || 1.6021E-13 || 1.6021E-12 || E,,k,,                             ||
|| Rest Mass                    || kg     || 9.1094E-31 || 1.6726E-27 || m,,0,,                             ||
|| Mass Energy                  || J      || 8.1871E-14 || 1.5033E-10 || E,,0,,=m,,0,,c^2^                  ||
|| Relativistic Momentum        || kg m/s || 7.60E-22   || 7.34E-20   || p=sqrt( 2E,,0,,E,,k,,+E,,k,,^2^)/c ||
|| Lorentz Factor               ||        || 2.957      || 1.0107     || gamma=1/sqrt(1-(v/c)^2^)           ||
|| Velocity                     || m/s    || 2.82E+08   || 4.34E+07   || v=pc^2^/(E,,k,,+E,,0,,)            ||
|| "Relativistic Mass"          || kg     || 2.69E-30   || 1.69E-27   || m,,r,,=m,,0,, gamma                ||
|| Gyration Period/Field        || T-s    || 1.06E-10   || 6.63E-08   || 2pi m,,r,, / q                     ||
|| Gyration Period @  0 degrees || s      || 4.41E-06   || 2.77E-03   || Period = 2pi m,,r,, / q B,,lat0,,  ||
|| Gyration Period @ 90 degrees || s      || 2.21E-06   || 1.39E-03   || Period = 2pi m,,r,, / q B,,lat90,, ||
|| Gyration Period from table   || s      || _1E-5_     || _7E-3_     || 10000nT, 2800km altitude B,,lat0,,??? ||

Calculations based on the equations in Pisacane [3] and the equations
for relativistic momentum and energy scattered around Wikipedia.  

Without the
pitch angle and the L value (or the magnetic latitude), I can't guess at the
bounce period (there are values that yield the above results).  Plausible
values of pitch angle yield gyration radii that are larger than those for 500km
in the table.  

The 20000km numbers ( the altitude of most nav-sats ) are plausible.

What am I missing here?

=== References: ===

[1] [[ http://www.everyspec.com/ESA/download.php?spec=ECSS-E-10-04A.014020.pdf | ECSS-E-10-04A,     21 January  2000, Table 28,  page 94 ]]

[2] [[ http://www.spacewx.com/Docs/ECSS-E-ST-10-04C_15Nov2008.pdf | ECSS-E-ST-10-04C, 15 November 2008, Table I-1, page 162 ]]

[3] [[ http://books.google.com/books?id=se-QKAAACAAJ | "The Space Environment and Its Effects on Space Systems", Vincent L. Pisacane, AIAA 2008, Table 6.5, page 135 ]]