Why do meteors detected by radio scatter appear not have Doppler shifts above 100 Hz but airplanes and satellites do?

If you mean rewrite the equations and symbols using only ordinary ASCII characters, here it is.

The key point is that meteor scatter does have Doppler shift. But unlike an aircraft or satellite, you usually aren’t receiving a reflection from the rapidly moving meteor itself. You are receiving a signal scattered from the ionised trail that the meteor leaves behind.

For a 148.048 MHz meteor-scatter system, this makes a very big difference.

Aircraft and satellites

An aircraft or satellite acts rather like a moving radio mirror. As it moves towards or away from you, the radio path length changes and produces Doppler shift.

The approximate Doppler shift is:

Doppler shift = (radial velocity / speed of light) x frequency

At 148 MHz, an object moving radially at 100 m/s gives approximately:

(100 / 300,000,000) x 148,000,000

= 49 Hz

For a reflected signal, the geometry can approximately double this in a simple head-on situation:

100 m/s -> approximately 100 Hz Doppler

So an aircraft travelling at around 250 m/s can easily produce hundreds of Hz of Doppler shift.

A satellite travelling at several kilometres per second can produce several kHz.

But a meteor is much faster

A meteor may be travelling at:

11 to 72 km/s

So you might expect a huge Doppler shift.

The reason you usually don’t see this is that you aren’t detecting the meteor itself.

Think of it like this:

                     METEOR
                       *
                       ---------> 30 km/s
                      /
                     /
-------------------------------------------------
       IONISED TRAIL LEFT BEHIND
-------------------------------------------------

Transmitter                               Receiver
    |                                        |
    |-------------- radio path --------------|

The meteor races onwards, but the ionised trail is left behind in the atmosphere.

A section of that trail might therefore be moving at only:

20 m/s
30 m/s
50 m/s
etc.

because its movement is primarily due to atmospheric winds and movement of the ionised gas.

At 148 MHz:

20 m/s -> about 10 Hz
50 m/s -> about 25 Hz
100 m/s -> about 49 Hz

Therefore it is perfectly reasonable for the meteor echoes you detect to remain within roughly 100 Hz of the transmitter frequency.

Compare this with an aircraft

AIRCRAFT

              [AIRCRAFT]
                  ------>
                 250 m/s

Transmitter  --------X--------> Receiver
                     ^
                     |
              moving reflector


METEOR

                         * ------>
                         meteor
                         30 km/s

             ====================
                ionised trail
             ====================
                    ^
                    |
              radio scattering
              from relatively
              stationary plasma

Transmitter ----------------------> Receiver

The important difference is:

AIRCRAFT
moving object
     |
     v
moving reflector
     |
     v
large Doppler


METEOR
very fast object
     |
     v
creates ionised trail
     |
     v
trail remains behind
     |
     v
relatively slow reflector/scatterer
     |
     v
small Doppler

There is an exception: meteor head echoes

If you detect the plasma immediately surrounding the moving meteor itself, rather than its trail, very large Doppler shifts are possible.

For a meteor travelling at 30 km/s:

velocity = 30,000 m/s

Doppler shift
= (30,000 / 300,000,000) x 148,000,000

= about 14,800 Hz

So a meteor-head echo could potentially be displaced by many kHz.

The distinction is therefore:

Aircraft       -> moving aircraft       -> 100s of Hz
Satellite      -> moving satellite      -> several kHz
Meteor trail   -> slow-moving plasma    -> usually 10s of Hz
Meteor head    -> fast-moving plasma    -> potentially many kHz

So “meteors don’t have Doppler shifts above 100 Hz” isn’t quite correct.

For ordinary meteor scatter, you are mainly detecting the slow-moving ionised trail, not the meteor travelling at tens of kilometres per second. That’s why your 148.048 MHz meteor signals can have very little Doppler while aircraft and satellites crossing the same receiver display can show much larger Doppler shifts.