To Androcles and Henry: Ballistic Doppler Shift Equation

From: Thomas Wong (nonfunctional_email_at_comcast.net)
Date: 01/11/05 

Date: 11 Jan 2005 05:14:51 -0800

Hi, Everybody!

I'm in my ultrafast spaceship traveling with my buddies Androcles and
Henri on a tourist trip to Uranus. It will take us only a few hours to
reach our destination, because our ship is capable of reaching NAFAL
(nearly-as-fast-as-light) velocities. We're in no real hurry though,
and we don't want to waste our supply of antimatter fuel, so right now
the speedometer says that we're driving slowly at only 35,940 km/s away
from Earth.

The driver gets to choose the radio station. I'm in the driver's seat
so I tune the radio to my favorite Houston oldies radio station KLDE-FM
(107.5).

Unfortunately, what is coming out of the speakers is COUNTRY!

Ahah, I know what is going on! Doppler shift!

Out of curiosity, I want to find out what station I'm listening to.

The relativistic Doppler shift equation is
f/f_0 = sqrt((1-v/c)/(1+v/c))
and when I plug the spaceship velocity into the equation, it tells me
that I'm tuned to KHYT (95.3).

Androcles looks at me sort of funny.

Henri screws his mouth up.

"Uh, Tom," says Androcles. "The relativistic Doppler shift equation is
wrong. Light travels ballistically."

To Androcles and Henri:

1) What is the Ballistic Doppler Shift equation for this case?
2) What is the speed of light from the radio stations relative to me?
3) What frequency on Earth am I tuned to?
4) What is the wavelength of the radio waves that I am receiving?
5) What station am I listening to?

Finally,
Instead of driving away from the Earth in my spaceship, I attach a huge
Bergenholm drive to the Earth and PUSH Earth away from my stationary
spaceship at a speed of 34,840 km/s.
1') What is the Ballistic Doppler Shift equation for this case?
2') What is the speed of light from the radio stations relative to me?
3') What frequency on Earth am I tuned to?
4') What is the wavelength of the radio waves that I am receiving?
5') What station am I listening to?

Thanks, buddies.

Tom