An observer is moving toward two co-orbiting binary stars at v = 0.8c.
The orbital plane of the stars is perpendicular to the line of sight.
At regular intervals one of the stars emits a radio blip to say that one
orbit has been completed. Let's assume that the frequency of that signal
is once per (earth) month in their frame.
Because the observer is travelling toward the stars, there should be an
increase in the frequency of that signal, implying to the observer that
the stars are orbiting faster than they say they are. (perhaps even
faster than c?)
Otoh, special relativity would seem to slow down that period.
A little help would be appreciated.

thanks
JH

Jim Hutton wrote:
An observer is moving toward two co-orbiting binary stars at v = 0.8c.
The orbital plane of the stars is perpendicular to the line of sight.
At regular intervals one of the stars emits a radio blip to say that one
orbit has been completed. Let's assume that the frequency of that signal
is once per (earth) month in their frame.
Because the observer is travelling toward the stars, there should be an
increase in the frequency of that signal,

What's the precise argument here?


implying to the observer that
the stars are orbiting faster than they say they are. (perhaps even
faster than c?)
Otoh, special relativity would seem to slow down that period.

Why?


Bye,
Bjoern

"Jim Hutton" wrote in message ...
An observer is moving toward two co-orbiting binary stars at v = 0.8c.
The orbital plane of the stars is perpendicular to the line of sight.
At regular intervals one of the stars emits a radio blip to say that one
orbit has been completed. Let's assume that the frequency of that signal
is once per (earth) month in their frame.
Because the observer is travelling toward the stars, there should be an
increase in the frequency of that signal, implying to the observer that
the stars are orbiting faster than they say they are. (perhaps even
faster than c?)
Otoh, special relativity would seem to slow down that period.
A little help would be appreciated.

The increase of frequency is a Doppler effect.

Consider a signal event (S) and the event (R) of the light of
the signal reaching the observer.
The time of event R is simply the clockreading of the
observer's clock when he sees the light. Let's call this time
t_R.
The time of the event S however is something else. One must
know how far away the event S took place to know "when"
it took place. Let's call the time (according to the observer)
of the signal event t_S. It is clear that t_S t_R.
Let's also call the time of the event in the frame of the orbit t.

Now consider two signal events S1 and S2, and likewise
the events R1 and R2 when the observer sees the signals.
Let's call the times of the signal events t_S1 and t_S2,
and let's call the times of the receptions of the signals
t_R1 and t_R2. In the frame of the orbital plane the signals
take place at times t1 and t2

Special relativity says that the connection between
t_S2 - t_S1 and t2 - t1 is given by
t_S2 - t_S1 = (t2 - t1) / sqrt(1-v^2/c^2)
This is the time dilation. You see that
t_S2 - t_S1 (t2 - t1)

It also gives the connection between t_R2 - t_R1
and t2 - t1 as follows:
t_R2 - t_R1 = (t2 - t1) * sqrt(1+v/c)/sqrt(1-v/c)
where v is taken positve for a receding source.
So if the source is approaching, you see that v 0
and you see
t_R2 - t_R1 (t2 - t1)
This is the so-called relativistic Doppler shift.

hth

Dirk Vdm

"Jim Hutton" wrote in message
...
An observer is moving toward two co-orbiting binary stars at v = 0.8c.
The orbital plane of the stars is perpendicular to the line of sight.
At regular intervals one of the stars emits a radio blip to say that one
orbit has been completed. Let's assume that the frequency of that signal
is once per (earth) month in their frame.
Because the observer is travelling toward the stars, there should be an
increase in the frequency of that signal, implying to the observer that
the stars are orbiting faster than they say they are. (perhaps even
faster than c?)
Otoh, special relativity would seem to slow down that period.
A little help would be appreciated.

thanks
JH

Doppler shift is linear in v / c and depends upon the direction of the
relative velocity between source and detector. Relativistic time dilation
isn't linear in v / c and depends only upon the magnitude of the relative
velocity.

If the velocity vector, v, of the source is transverse to the line between
source and detector, then the Doppler shift is due entirely to relativistic
time dilation:

f(detector) / f(sorce) = 1 / gamma = sqrt[ 1 - (v / c)^2 ]

If the velocity vector, v, of the source encloses an angle, theta, WRT
the line between source and detector, then the Doppler shift is

f(detector) / f(sorce) = [ 1 - (v / c) cos(theta) ] / gamma

Time dilation is independent of "theta" and is always present.

[Old Man]