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Size: 3957
Comment:
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Size: 4065
Comment:
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| Deletions are marked like this. | Additions are marked like this. |
| Line 34: | Line 34: |
| || L @ 0 degrees magnetic || || 1.078 || || L @ 90 degrees magnetic || || infinite || || B @ 0 degrees magnetic || Tesla || 2.40E-05 || || B @ 90 degrees magnetic || Tesla || 4.79E-05 || |
|| L @ 0 degrees magnetic latitude || || 1.078 || || L @ 90 degrees magnetic latitude || || infinite || || B @ 0 degrees magnetic latitude || Tesla || 2.40E-05 || || B @ 90 degrees magnetic latitude || Tesla || 4.79E-05 || |
| Line 39: | Line 39: |
| ||||<|2> |||| Particle || || electron || proton || || Kinetic Energy || MeV || 1 || 10 || || Kinetic Energy || J || 1.6021E-13 || 1.6021E-12 || || Mass || kg || 9.1094E-31 || 1.6726E-27 || || Mass Energy || J || 8.1871E-14 || 1.5033E-10 || || Relativistic Momentum || kg m/s || 7.60E-22 || 7.34E-20 || || Lorentz Factor || || 2.957 || 1.0107 || || Velocity || m/s || 2.82E+08 || 4.34E+07 || || "Relativistic Mass" || kg || 2.69E-30 || 1.69E-27 || || Gyr Period/Field || T-s || 1.06E-10 || 6.63E-08 || || Gyr Period @ 0 degrees || s || 4.41E-06 || 2.77E-03 || || Gyr Period @ 90 degrees || s || 2.21E-06 || 1.39E-03 || || Gyr Period from table || s || 1E-5 || 7E-3 || |
||||<|2> |||| Particle || || electron || proton || || Kinetic Energy || MeV || 1 || 10 || || Kinetic Energy || J || 1.6021E-13 || 1.6021E-12 || || Mass || kg || 9.1094E-31 || 1.6726E-27 || || Mass Energy || J || 8.1871E-14 || 1.5033E-10 || || Relativistic Momentum || kg m/s || 7.60E-22 || 7.34E-20 || || Lorentz Factor || || 2.957 || 1.0107 || || Velocity || m/s || 2.82E+08 || 4.34E+07 || || "Relativistic Mass" || kg || 2.69E-30 || 1.69E-27 || || Gyration Period/Field || T-s || 1.06E-10 || 6.63E-08 || || Gyration Period @ 0 degrees || s || 4.41E-06 || 2.77E-03 || || Gyration Period @ 90 degrees || s || 2.21E-06 || 1.39E-03 || || Gyration Period from table || s || 1E-5 || 7E-3 || |
| Line 58: | Line 58: |
| for relativistic momentum and energy on Wikipedia | for relativistic momentum and energy scattered around Wikipedia. |
| Line 68: | Line 68: |
| [3] "The Space Environment and Its Effects on Space Systems", Vincent L. Piscane, AIAA 2008, Table 6.5, page 135 | [3] "The Space Environment and Its Effects on Space Systems", Vincent L. Pisacane, AIAA 2008, Table 6.5, page 135 |
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.
|
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 |
Radius of gyration (km) |
||
@ 500 km |
0.6 |
50 |
@ 20000 km |
10 |
880 |
Gyration period (s) |
||
@ 500 km |
1E-5 |
7E-3 |
@ 20000 km |
2E-4 |
0.13 |
Bounce period (s) |
||
@ 500 km |
0.1 |
0.65 |
@ 20000 km |
0.3 |
1.7 |
Longitudinal drift period (min) |
||
@ 500 km |
10 |
3 |
@ 20000 km |
3.5 |
1.1 |
Constants:
B_0_ Magnetic field constant |
Tesla |
3.0037E-05 |
Unit charge |
Colombs |
1.6021E-19 |
Joules per MeV |
J/MeV |
1.6021E-13 |
Re Earth radius |
m |
6378210.00 |
C Speed of Light |
m/s |
2.9979E+08 |
Let's compute some numbers at 500km altitude:
L @ 0 degrees magnetic latitude |
|
1.078 |
L @ 90 degrees magnetic latitude |
|
infinite |
B @ 0 degrees magnetic latitude |
Tesla |
2.40E-05 |
B @ 90 degrees magnetic latitude |
Tesla |
4.79E-05 |
|
Particle |
||
electron |
proton |
||
Kinetic Energy |
MeV |
1 |
10 |
Kinetic Energy |
J |
1.6021E-13 |
1.6021E-12 |
Mass |
kg |
9.1094E-31 |
1.6726E-27 |
Mass Energy |
J |
8.1871E-14 |
1.5033E-10 |
Relativistic Momentum |
kg m/s |
7.60E-22 |
7.34E-20 |
Lorentz Factor |
|
2.957 |
1.0107 |
Velocity |
m/s |
2.82E+08 |
4.34E+07 |
"Relativistic Mass" |
kg |
2.69E-30 |
1.69E-27 |
Gyration Period/Field |
T-s |
1.06E-10 |
6.63E-08 |
Gyration Period @ 0 degrees |
s |
4.41E-06 |
2.77E-03 |
Gyration Period @ 90 degrees |
s |
2.21E-06 |
1.39E-03 |
Gyration Period from table |
s |
1E-5 |
7E-3 |
So, depending on the magnetic latitude of this "typical particle", the table values for the gyration period are between 2.3 and 5.0 too large.
Calculations based on the equations in Pisacane [3] and the equations for relativistic momentum and energy scattered around Wikipedia.
What am I missing here?
References:
[1] ECSS-E-10-04A, 21 January 2000, Table 28, page 94
[2] ECSS-E-ST-10-04C, 15 November 2008, Table I-1, page 162
[3] "The Space Environment and Its Effects on Space Systems", Vincent L. Pisacane, AIAA 2008, Table 6.5, page 135