Apparent path length

Assuming constant beginning and end altitudes (H_b, H_e) for meteors belonging to a certain shower one can calculate the expected apparent path length l for members of the shower depending on the elevation of the radiant h_R, the elevation of the start point h_b, and the angular distance between the radiant and the start point D_b:

For given beginning and end altitudes, l depends on three quantities: h_R, h_b, and D_b. To visualize this dependence we would have to construct a 4-dimensional diagram which is impossible. This means that the criterion is quite difficult to handle. But calculating l for several combinations of beginning/ending altitudes one finds:

This means that the criterion l can be used favourably in the vicinity of the radiant. In that region shower meteors distinguish themselves from sporadics by their short paths. Bearing in mind that the end altitude depends on the particle mass and material it is opportune to assume it is such that the calculated l is considered to be the upper limit for shower membership. Thus it was assumed H_b = 100 km and H_e = 80 km. The result is shown in Figure 11.

Figure 11 - The quotient D_b / l for D_b < 30° as a function of h_b for several elevations of the radiant h_R. Calculation was carried out using H_b = 100 km, and H_e = 80 km.

It can be seen that radiants having low elevations produce long meteor paths (small value of D_b / l). The higher the meteor appears in the sky the closer it is to the observer, and thus, the true trail length is seen over a larger angle (apparent path length l). The application of the quantities shown in Figure 11 for shower association is problematic since end altitudes can vary greatly and the path length is much more affected by plotting errors than the direction. Therefore, we can establish only a general rule:

For radiant elevations higher than 30° the apparent path length l of a shower meteor amounts at most to half the distance from the radiant to the start point.

Consequently, the distance between radiant and start point of a plotted meteor on the chart has to be at least twice as long as the meteor path itself if the meteor is a suspected shower member. This rule is not valid for fireballs which generally penetrate deeper into the atmosphere and thus produce longer paths.

Looking at Figure 11, the formulation of the rule seems to be too weak, since factors of 3-5 will be valid for most meteors, but in strengthening the rule there is the danger of classifying a considerable number of shower meteors in the vicinity of the radiant as sporadics, due to short paths being plotted as too long. Experience shows that a factor of two is strong enough for distinguishing sporadic meteors meeting the criteria of path direction and angular velocity, within certain error limits, from real shower meteors.