Of Particular Significance

Measuring the Speed of a Meteor

It’s not difficult to estimate the speed of meteors, and doing so is an important critical step in determining the distance to the Sun without using a telescope or any fancy math. There are basically two steps.

  1. We can figure out how high a meteor is using parallax. If two people on the ground, a known distance apart, see a meteor in slightly different places on the sky, the difference can be used to determine how far away the meteor is.
    • (If we’re feeling a bit lazy, we could just determine meteors’ average heights, rather than figuring the height of each meteor.)
  2. We can estimate how quickly a meteor travels across the sky — the rate at which its position on the sky changes.

Then we can combine these two pieces of information to obtain an estimate for a meteor’s speed.

Estimating A Meteor’s Height

If you and a friend, located a few tens of miles apart, go meteor watching in your separate dark locations, you will see some of the same meteors but from different perspectives. To illustrate the idea in its simplest form, suppose you observe a meteor that begins its path directly above you. Your friend will see the same meteor at the same time, but at a different place on the sky, not overhead but skewed in your direction by an angle α from the vertical, as illustrated in Fig. 1. Then the height of the meteor, in terms of the distance L between you and the angle α, is

  • h = L / tan α

as long as L is small enough that the curvature of the Earth has only a minor effect on the calculation.

Figure 1: A meteor (yellow dot) is directly over your head, but from your friend’s perspective, it is displaced from vertical by an angle 𝛼. Then the height of the meteor h is the distance L between you and your friend divided by the tangent of 𝛼.

This “parallax” method can be generalized to meteors at other locations in the sky, which aren’t overhead of either of you. But we needn’t go through the details here. The point is that you and your friend can estimate the height of meteors that you both observe, and the accuracy of your estimate just depends on how carefully you use and measure parallax.

In fact the first known estimate of a meteor’s height, using precisely this method, was carried out by Edmund Halley (of “Halley’s Comet” fame) in 1714. He took a meteor that had been well-measured by two people in different locations, and estimated that the meteor was at an altitude of 40 to 50 miles (65 to 80 km). (In fact most meteors start a bit higher.)

Estimating a Meteor’s Speed

Now that we know a meteor’s height, it’s not hard to find its speed, using the rate at which it seems to cross the sky.

This is a little complicated because a meteor’s height changes as it falls. Also, a meteor slows down due to the friction that makes it glow, so its speed isn’t actually constant.

But we can make our lives simpler by focusing attention on “Earth-grazers”, which are most common when the radiant of a meteor shower (the direction from which the meteors are coming) is near the horizon, from our perspective. (For reasons discussed here, these are most often found in the sky before midnight — which is convenient for those who don’t want to stay up all night.) These meteors hit the atmosphere sideways, as in Fig. 2, so

  • their paths keep them at high altitudes for a long time
  • since they remain high, where the air is thin and friction is low, their speeds slow only gradually
  • this allows them to make a long trail across the sky, making it easy to measure the rate at which they cross it.

Here’s a nice video of an Earth-grazer; and here’s another. Note that they take seconds, not minutes or fractions of a second, to cross the sky.

Figure 2: An Earth-grazer meteor (orange line) has an altitude that varies relatively little, and leaves a much longer track, compared to a meteor coming nearly straight toward the Earth.

The basic principle of finding a meteor’s speed is easiest to illustrate if we consider an idealized situation similar to that of an Earth-grazer: a meteor whose height is constant, as in Fig. 2. We will again assume that the curvature of the Earth isn’t a very important effect. (It’s not hard to include that curvature if we need to, but it complicates the discussion.)

Suppose that at a certain moment the meteor is directly overhead, and after a certain amount of time T (perhaps one second) the meteor has moved so that it appears to be at an angle 𝛃 relative to the vertical. Then the distance D that the meteor has traveled is its height h (which we know from parallax as described above) multiplied by tan 𝛃. The speed of the meteor, vm , is then D/T, and thus

  • vm ≈ h tan 𝛃 / T

I put an “approximately equal to” sign here because our assumption that the meteor travels is at a constant altitude won’t be exactly true of any real meteor.

Figure 3: A meteor that moves horizontally, and appears to move from overhead to an angle 𝛃 with the vertical, has traveled a distance D = h tan 𝛃 ,

If you carry this exercise out, you will find that all meteors that cross the sky are traveling below 100 km per second (60 miles per second.) Let me try to convince you of this, just from what you may already have seen of meteors.

A Quick Check of Meteor Speeds

If you want now to measure meteors’ speeds, its time to go outside and look up, especially on nights with meteor showers where meteors are both more abundant and more informative.

But before we send you out into the darkness, let’s quickly convince ourselves that this number I keep quoting — that meteor speeds are tens of km per second — makes sense, based on something else that we can see in the sky.

The international space station (ISS) is easily observed crossing the night sky with the help of NASA’s website that lists when you can see it pass over your area. Depending on exactly what path the ISS takes, it is visible for as much as seven to eight minutes. In particular, when it goes overhead, it tends to be visible for the longest time. For example, in Cleveland, Ohio, the ISS will be visible on February 2nd, 2024 for over 7 minutes, during which it will travel from horizon (10 degrees) to nearly overhead (87 degrees) to nearly the other horizon (10 degrees).

Fri Feb 2, 6:19 PM7 min87°10° above NW10° above SE

As we were able to learn ourselves, a near-Earth satellite in a circular orbit moves at about 5 miles (8 km) per second. (The ISS is about 250 miles (400 km) above the Earth’s surface, and the fact that it takes it 3.5 minutes to go from overhead to horizon can be used to confirm that its speed is, very roughly, about 10 km per second — and definitely neither 100 km per second nor 1 km per second!)

Since meteors are often at 100 km high, they are roughly four times closer than the space station, so if they moved at the same speed as the space station, they’d appear to cross the sky four times faster — in nearly two minutes, rather than seven or eight. But in fact, as you can see in the Earth grazer videos that I linked to above, the rare meteor that crosses the whole sky, horizon to horizon, takes ten to twenty seconds to do it. That’s 1/12th to 1/6th of the two minutes that would elapse if the meteor were moving at ISS speeds. And so we learn that meteors must be moving 6 to 12 times faster than the space station — and thus, typically, 50 to 100 km per second, confirming the estimate that I’ve been giving you.

To learn how to measure the Earth’s speed around the Sun from meteors’ speeds, click here.

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