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Meteor Orbits
If the space of the solar system be equally filled with meteors throughout, or if they diminish as one goes out from the Sun according to any rational law, their average speed of encounter with the Earth would be nearly parabolic.
If they were travelling in orbits like those of the short-period comets, that is with their aphelia at Jupiter’s orbit and their perihelia at or within the Earth’s, their major axes would lie between 6.2 and 5.2. If we suppose their perihelion distances to be equally distributed according to distance, we have for the mean a major axis of 5.7. Their velocity, then, at the point where they cross the Earth’s track would be given by
v² = µ(2/1 - 1/2.85),
in which µ = 18.5² in miles per second = 342.25,
whence v = 23.76 in miles per second.
Suppose them to be approaching the Earth indifferently from all directions.
At sunset the zenith faces the Earth’s quit; at sunrise the Earth’s goal. Let θ be the real angle of the meteor’s approach reckoned from the Earth’s quit; θ₁ the apparent angle due to compounding the meteor’s velocity-direction with that of the Earth. Then those approaching it at any angle 0 less than that which makes θ₁ = 90° will be visible at sunset; those at a greater angle, at sunrise. The angle 01 is given by the relation,
| a | ||
| cos θ₁ | = | + —— , |
| x |