K_h says...


"Koobee Wublee" wrote

** f' / f = (1 + [v] * [c]) / sqrt(1 - v^2 / c^2)

Look at the obvious problem with this equation. You have V and C as velocity
vectors which means their dot product is in units of meters squared per second
squared, that is, (m/sec)^2. Then you are adding that to the dimensionless
number 1 in your numerator (1+[v]*[c]). In physics you cannot add quantities
that are in different units. Suppose [v]*[c] is 2x10^16(m/sec)^2, just how do
you propose to add that to the dimensionless number 1? In
physics you cannot add 6 kilograms to 1 meter just like you cannot
add 3(m/sec)^2 to a dimensionless number.

Uh, Koobee is not that clueless. I'm sure it was a typo.
What he meant to write was

f'/f = (1+v/c)/sqrt-(1-v^2/c^2)

for the parallel Doppler case, and

f'/f = 1/sqrt(1 - v^2/c^2)

for the transverse Doppler case.

--
Daryl McCullough
Ithaca, NY