Angular velocity

Meteors of a given shower start to emit light at similar heights above the Earth's surface. Their velocities are also alike, with only small differences. The deceleration on the luminous path through the atmosphere can be neglected for ordinary meteors; their velocity is reduced by a few percent only. For our purposes we can assume that shower meteors move parallel to each other with a constant velocity.

Thus the apparent angular velocity omega of a shower meteor (in degrees per second) can be calculated by the framed formula below depending on the pre-atmospheric velocity V_infty (km/s), the elevation h_b (degrees) and altitude H_b (km) of its start point, and the angular distance between its end point and the radiant D_e (degrees).

Figure 10 - The trajectory of a meteor in the atmosphere. From this geometric situation we can determine the angular velocity omega of a shower meteor with a known atmospheric entry velocity V.

With l being the apparent path length of the meteor and s its true trail length.

For apparent path lengths l shorter than ~30° we find:

Finally, we can write:

The angular velocity omega of a shower meteor is thus well defined for any point in the sky. It is a strict criterion used for shower association.

In the below table the angular velocities omega for different entry velocities V have been calculated. Since the beginning altitude H_b depends mainly on V, characteristic beginning altitudes for individual geocentric velocities were assumed in the calculations.

The following table is used to determine the expected angular velocity of shower meteors. For interpolation of values not directly included in the table, please refer to the examples given below the table.

             V=20 km/s  H_b=100 km      |       V=25 km/s  H_b=100 km
h_b=    10°    20°    40°    60°    90° |  10°    20°    40°    60°    90°
                                        |
D= 5°  0.2    0.3    0.6    0.9    1.0  | 0.2    0.4    0.8    1.1    1.3
  10°  0.3    0.7    1.3    1.7    2.0  | 0.4    0.9    1.6    2.2    2.5
  20°  0.7    1.3    2.5    3.4    3.9  | 0.9    1.7    3.2    4.3    4.9
  40°  1.3    2.5    4.7    6.3    7.3  | 1.6    3.2    5.9    8.0    9.3
  60°  1.7    3.4    6.3    8.5    9.8  | 2.2    4.3    8.0   11     13
  90°  2.0    3.9    7.3    9.8   11    | 2.5    4.9    9.3   13     14

             V=30 km/s  H_b=100 km      |       V=35 km/s  H_b=100 km
h_b=    10°    20°    40°    60°    90° |  10°    20°    40°    60°    90°
                                        |
D= 5°  0.3    0.5    1.0    1.4    1.6  | 0.3    0.6    1.1    1.5    1.7
  10°  0.5    1.1    2.0    2.7    3.1  | 0.6    1.2    2.2    3.0    3.4
  20°  1.1    2.1    4.0    5.3    6.2  | 1.2    2.3    4.3    5.8    6.7
  40°  2.0    4.0    7.4   10     12    | 2.2    4.3    8.2   11     13
  60°  2.7    5.3   10     14     16    | 3.0    5.8   11     15     17
  90°  3.1    6.2   12     16     18    | 3.4    6.7   13     17     20

             V=40 km/s  H_b=100 km      |       V=50 km/s  H_b=110 km
h_b=    10°    20°    40°    60°    90° |  10°    20°    40°     60°   90°
                                        |
D= 5°  0.3    0.7    1.3    1.7    2.0  | 0.4    0.8    1.5    2.0    2.3
  10°  0.7    1.4    2.6    3.5    4.0  | 0.8    1.6    2.9    3.9    4.6
  20°  1.4    2.7    5.0    6.8    7.9  | 1.6    3.1    5.8    7.8    9.0
  40°  2.6    5.0    9.5   13     15    | 2.9    5.8   11     15     17
  60°  3.5    6.8   13     17     20    | 3.9    7.8   15     20     23
  90°  4.0    7.9   15     20     23    | 4.6    9.0   17     23     26

             V=60 km/s  H_b=115 km      |       V=66 km/s  H_b=115 km
h_b=    10°    20°    40°    60°    90° |  10°    20°    40°     60°   90°
                                        |
D= 5°  0.5    0.9    1.7    2.3    2.6  | 0.5    1.0    1.9    2.5    2.9
  10°  0.9    1.8    3.4    4.5    5.2  | 1.0    2.0    3.7    5.0    5.8
  20°  1.8    3.5    6.7    9.0   10    | 2.0    3.9    7.3   10     11
  40°  3.7    6.7   13     17     20    | 3.7    7.3   14     18     21
  60°  4.6    9.0   17     23     26    | 5.0   10     18     25     29
  90°  5.3   10     20     26     30    | 5.8   11     21     29     33

             V=70 km/s  H_b=126 km
h_b=    10°    20°    40°    60°    90°

D=5°   0.5    0.9    1.8    2.4    2.8
  10°  1.0    1.9    3.6    4.8    5.5
  20°  1.9    3.7    7.0    9.4   11
  40°  3.6    7.0   13     18     21
  60°  4.8    9.4   18     24     28
  90°  5.5   11     21     28     32

Examples:
1. Virginid  V=35 km/s   h_b=60°   D_e=40°   omega=11°/s
2. Orionid   V=66 km/s   h_b=30°   D_e=60°   omega~14°/s
3. Ursid     V=33 km/s   h_b=50°   D_e=30°   omega~ 7°/s