On 11/15/2011 12:56 AM, Szczepan Bialek wrote:
"Jim napisal w wiadomosci
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You mean when earth is generally heading "towards" the galactic center vs
when earth is heading "away" from the galactic center?

Yes. But on the Earth orbit are places when this speed is 0.5 km/s (only
rotation) or 30 km/s. (orbital speed).

People doing deep space navigation deal with this all the time, since
navigation is done by measuring the frequency of the received signal from
the spacecraft. There's nothing special about it. spacecraft on some
heliocentric trajectory, Earth on a different heliocentric trajectory.

Like the Earth and Mars.

Yes, and, for instance, they measure the Doppler shift in the signals
radiated from spacecraft/rovers in orbit/on the surface of Mars as they
arrive at earth.

As expected, the Doppler has several components: one from the rotation
of Earth, one from the rotation of Mars (for a surface asset), and one
from the relative motion of Mars and Earth (which is periodic with about
a 2 year, 2 month period)

No surprises, nothing unusual. In fact, *tiny* variations in the
Doppler are used to compute the orbit around planets, and from that,
infer the internal structure of the planet. Juno is going to Jupiter
right now to do this, and the Doppler will be measured with a precision
of about 1 part in 1E15 (measured over 100-1000 seconds).



Measure frequency shift, they use to determine spacecraft trajectory by
applying (mostly) Newtonian physics (you do have to use relativistic
corrections to get the last gnat's eyelash of precision).

They confirm the diurnal changings in the frequency. But what with the
annual?

All changes in frequency, of course. Load up the SPICE kernels, run the
numerical integration, and the expected frequency pops out.



Since you only get to measure in one direction, you have to make
assumptions about what's going on in the other directions, (e.g. cross
range), which can lead to disasters (Mars Climate Orbiter, most recently).

You can do various forms of VLBI and DeltaDOR to get some cross range
information, but nothing as good as what you're getting for range (where
velocity and range are measured to mm/s and cm sorts of accuracy)

Naw are the spacecraft at distances almost like stars. They are not on
heliocentric trajectory.

All spacecraft that humans have launched are on some form of either
planetary centric or heliocentric trajectory or a combination of both.
In any case, they are computable (viz. Gauss) and measureable.




So I repeat my question:
" I have found the link:
http://chaos.swarthmore.edu/courses/...er_Anomaly.pdf

""It is also possible to infer the position in the sky of a
spacecraft from the Doppler data. This is accomplished by

examining the diurnal variation imparted to the Doppler shift

by the Earth's rotation. As the ground station rotates underneath

a spacecraft, the Doppler shift is modulated by a sinusoid."


That's somewhat of an over simplification, but it's essentially true.

The paper describes the technique used to measure the frequency.. A
signal is generated on the ground at 2.11 GHz, locked to a hydrogen
maser. that signal is radiated to the spacecraft, which uses a phase
locked loop to track it. The spacecraft sends back a signal with a
frequency/phase ratio of exactly 240/221 (i.e. about 2.29 GHz) which is
received on earth and compared with the same hydrogen maser.



Here they confirm the diurnal variation in the frequency.

Probably in this paper is also the answer for my question: "And what about
the 365 days period (annual variation in the frequency)?
Unfortunately I am not an expert in radio. Do you know the answer?

Do you want to know the magnitude of the shift? Earth's orbital velocity
is about 30km/s, so the fractional frequency change is 1 part in 1E4
(100ppm). That's huge compared to, for example, the change due to the
oscillator frequency aging. Considering that for deep space navigation,
frequencies are regularly measured these days to parts in 1E12, this is
something they deal with on a day to day basis at the Deep Space Network.


if you want more details, take a look at equations (3) through (6) on
page 11-12 of the 50 page paper you cited, which gives a nice detailed
explanation of all the factors they are taking into account. And, they
nicely note how you can use the models to implement theories of gravity
other than general relativity.

equation 4 describes the light time (which ties to doppler measurement)
and includes the relativistic corrections as well.

they take into account things you haven't mentioned such as changes in
the earth orientation (precession, for instance), changes in earth
rotation rate.

"In summary, this dynamical model accounts for a number
of post-Newtonian perturbations in the motions of the planets,
the Moon, and spacecraft. Light propagation is correct to
order c^-2. The equations of motion of extended celestial
bodies are valid to order c^-4. Indeed, this dynamical model
has been good enough to perform tests of general relativity
@28,51,52#."



I'd comment that if you read and understand the entire paper, you're
well on your way to really knowing how we do deep space navigation and
the myriad things that have an effect and must be taken into account.
They also have a VERY complete discussion of numerical computation effects.

They also do mention an annual sinusoid (not accounted for by simple
orbital motion) of 1.6E-8 cm/s^2... (about 0.012 Hz at 2.29GHz) (page
37) which they attribute to small problems in their modeling of the
solar system that are normally masked by other noise sources, but
because Pioneer makes such a good detector, you can find it.

I'll note that the anomaly identified in the paper has since been
analyzed extensively, and as I recall, once you take into account the
thermal radiation pressure with sufficient accuracy, you can account for it.

(there has been a substantial improvement in computational and modeling
capability in the last 10 years, since that paper was published) After
all, the paper says "Further experiment and analysis is obviously needed
to resolve this problem."