# Does communications with spacecraft red shift the further away they are?

As Voyager 1 and 2 proceed further away do the radio waves red shift (change frequency)?

If so, then don't we have to compensate for that red shift by modulating the frequency so that it arrives at the expected frequency at the destination?

Theoretical Example: if the spacecraft is expecting 5.0 GHz then doesn't Earth have to transmit at 5.2 GHz to allow for the red shift?

Or am I confusing issues?

• Red Shift is an artefact of velocity not distance. – Brian Tompsett - 汤莱恩 Apr 20 '16 at 13:23
• The question is valid and a bit deeper than meets the eye. Be careful with quick answers unless you know your cosmology! – uhoh Apr 20 '16 at 18:31
• Red-shift as a function of distance applies to stars (Hubble's Law), not to man-made objects. Due to the (more-or-less) even expansion of the universe, more distant stars are moving proportionally faster away from us than closer stars. But none of this applies to man-made objects, since they are way too close, and were not formed from the expanding matter of the early universe. – Reversed Engineer Apr 20 '16 at 19:33
• @DaveBoltman Well, you are looking at millihertz of Doppler shift due to expansion of the universe for the distances and frequencies involved in the OP's question. Valid, but totally overshadowed by the simple fact that the probes are still carrying a great deal of velocity relative to Earth after being cut loose from the boosters and their gravity slingshot maneuvers... – a CVn Apr 20 '16 at 19:47
• @DaveBoltman "doesn't apply because it's too close" or even "...way too close" is not usually how these things go. It applies. It's small. BOTH are true. – uhoh Apr 20 '16 at 20:08

No, at the distances we have sent any spacecraft or probe to, there is no need to compensate for redshift (the Doppler effect) because a spacecraft is far away. Doppler shift is an effect of relative velocity, not distance.

The Doppler effect is defined such that the frequency $f$ as observed by a receiver moving at velocity $v_r$ relative to a source moving at velocity $v_s$ and where the source is transmitting at frequency $f_0$ is $$f = \left( \frac{c + v_r}{c + v_s} \right) f_0$$

In the case of radio transmissions, $c$ is the speed of light. $v_r$ and $v_s$ are measured in some inertial (that's basically a fancy word for "non-moving") reference frame.

For a stationary sender or receiver, simply set $v_s = 0$ or $v_r = 0$ respectively. From this it is obvious how, when both sender and receiver are stationary (in an inertial reference frame), the transmitted frequency equals the received frequency.

As you can see, for a given type of transmission (such as a radio transmission), only the relative velocities of the sender and receiver and the transmission frequency affect the received frequency.

This effect is caused by the fact that when the sender is moving toward the receiver, each wave front is closer to its neighboring wave fronts than merely its frequency would warrant. Likewise, when the two are moving away from each other, each wave front is farther away from its neighbors. Colloquially, the transmission is being "pushed together" or "dragged apart" by the relative movement of the sender and receiver. This is observed as a change in frequency at the receiver.

The distance between the two do not play a role in this effect, and thus we do not need to compensate for Doppler shift merely because an object is far away. We do however have to compensate for Doppler shift because the object is moving relative to us. Of course, because spacecraft generally move at relatively high speeds relative to an Earth ground station, in spacecraft communications we often do need to pay attention to Doppler shift, regardless of whether they are close to or far from Earth.

For example, if the spacecraft is moving away from the Sun at 15 km/s (not unreasonable at all for interplanetary missions) and Earth happens to be moving in the opposite direction at 30 km/s (which it does once a year), and the spacecraft is transmitting on 5 GHz, the frequency as received on Earth will be $$f = \left( \frac{300~000~000 - 15~000}{300~000~000 + 30~000} \right) \times 5~000~000~000 \approx 4~999~250~075$$ or approximately 4999.25 MHz instead of 5000.00 MHz. Conversely, if we want the spacecraft to receive our transmission on 5000.00 MHz, then we need to transmit at approximately 5000.75 MHz. If we didn't compensate for Doppler shift, we would need a receiver bandpass filter bandwidth of nearly a megahertz; enough to cram in two or three broadcast FM stations.

It's also worth keeping in mind that this is an issue not just for deep space missions. The math is a bit more involved because of the trigonometry to calculate the absolute value of the velocity and if you want an absolute value also compensating for the planet's rotation, but the exact same principles apply when a low orbit spacecraft is communicating with a ground station or for that matter with a spacecraft in a different orbit.

If we were to send spacecraft to other galaxies or even far-away stars, then Doppler shift due to the expansion of the universe might start to actually matter. However, for as long as it can be argued whether we have even exited our own solar system, the relative velocities caused by expansion of the universe are of magnitudes that are completely irrelevant for practical radio communications. The expansion of the universe is given as Hubble's constant $H_0$, and the most recent estimate for its value is $67~800 \pm 770$ m/s per megaparsec. The Voyagers are about 134 and 110 AU away, respectively, which works out to $6.497 \times 10^{-10}$ and $5.333 \times 10^{-10}$ megaparsec. If my math is right, taking Voyager 1 because it is farther away, this means an observed expansion rate of about 0.00004405 m/s (44 µm/s) corresponding to a received frequency of $$\left( \frac{300~000~000}{300~000~000 + 0.00004405} \right) \times 5~000~000~000 = 4~999~999~999.999265833$$ or a Doppler shift of about 0.001 Hz when the transmitted frequency is exactly 5 GHz. In other words, valid in theory but completely negligible in practice.

• I realise that theoretically we need to compensate, but is it ever actually done in reality? Are today's spacecraft moving fast enough (still only a fraction of $c$, the driving part of that equation) that it's a real issue? – James Thorpe Apr 20 '16 at 15:36
• What about doppler shift caused by the expansion of space? Does that pose a significant enough effect to require adjusting? – gandalf3 Apr 20 '16 at 17:54
• @gandalf3 has a point - there is a 'red shift' due to the fact that every point is moving away from every other point (or at least so say smart people). The answer may be "it's really small and so no you don't need to compensate for it explicitly" but the answer is probably NOT "no, because it doesn't happen." Somebody just go look up the Hubble constant for us! – uhoh Apr 20 '16 at 18:37
• i did. Question is about red shift. You mix the term together with Doppler shift and create confusion. They are two totally different things. Why don't you remove everything about Doppler shift. The question was worded well. – uhoh Apr 20 '16 at 19:56
• @uhoh Redshift is the Doppler effect applied to light waves. Perhaps what you're trying to express is the difference between redshift due to velocity relative to the Earth, and redshift due to the expansion of the Universe? The original question is vague about which they're asking about, perhaps the OP doesn't know either. This answer properly covered both. – Schwern Apr 20 '16 at 22:24

Contrary to the other answers, distance from the earth does does cause/influence red-shift (albeit indirectly). The universe is expanding away from us, and the further away a point in space is, the faster the expansion is at that point. The expansion rate is rather regular and predictable at macroscopic scales, so scientists actually use red-shifts of hydrogen emission spectra for distant stars to gauge how far stars and galaxies are from us.

If you had a spacecraft very, very far away, the universe's relative expansion to us would cause signals between us and the craft to be redshifted.

The expansion rate of our universe is usually given as Hubble's constant -- $H_0 = 67.15 (km/s)/Mpc$. We can calculate the velocity of the universe's expansion at a given distance as $H_0$ * the distance away.

Plugging in a distance like the distance to the closest star in wolfram alpha, we get that between us and Alpha Centauri, the universe is expanding at a rate of 0.2 miles per hour, or 0.3 kilometers per hour.

This is probably much lower than the actual relative velocity between us and Alpha Centurai just due to the fact that we're moving in different directions! So redshift will not be a significant factor if we ever decide to communicate to Alpha Centauri -- our actual relative velocities due to our relative motion will be more significant.

At intergalactic differences things might start getting a bit more noticeable. Between us and andromeda, the universe is expanding at a rate of about 53 km/s, about 120 million miles per hour, or about one ten thousandths of the speed of light. This is still not really enough to be terribly significant, I believe, but it does give a good scale as to how distance necessarily affects relative velocity and, indirectly, redshift.

EDIT A comment was made that reminded me that while expansion is homogeneous at the macroscopic level, the metric expansion of space might behave as homogeneously at sub-lightyear levels. I'm not familiar enough with this topic to give a definitive answer as to what models could be useful here.

• Kudos for math! ...and quantitative answering!!! – uhoh Apr 20 '16 at 18:40
• check my math - I think that's 1 meter/sec at 4.4E+14 kilometers. At Neptune (4.5 billion km) that's an apparent (real?) velocity of 1.0E-05 meters/sec. For a 2GHz signal from earth received and rebroadcast (for doppler sounding) that's a shift of 0.001 Hz. Small, but real!, (real small). – uhoh Apr 20 '16 at 18:54
• @uhoh Looks like your math is correct; see my answer. – a CVn Apr 20 '16 at 19:44
• From Wikipedia: "However, the (expansion) model is valid only on large scales (roughly the scale of galaxy clusters and above). At smaller scales matter has become bound together under the influence of gravitational attraction and such things do not expand at the metric expansion rate as the universe ages. " IMO that means you wouldn't get a redshift from a probe at Alpha Centauri. – Hobbes Apr 20 '16 at 20:03
• @Hobbes that's about "the expansion model". It says that in gravitationally bound clusters of "star stuff" and other mass, their motion does not track the large scale expansion - roughly speaking because of their mutual gravitational interaction. It doesn't mean necessarily that space isn't expanding, it does mean (among other things) that if you want to measure the Hubble constant by measuring motion of "stuff", better choose points far enough apart that they are not appreciably interacting. Copy/pasting paragraphs about cosmology is not a good idea. – uhoh Apr 20 '16 at 20:17

Let me add to @Michael's answer by saying that this is also very much a factor when communicating with earth-orbiting satellites. For instance, the ISS signal bounces off a geostationary communications satellite before it (the signal) gets to the ground. If I recall correctly, these two spacecraft can differ in velocity up to 7 km/s. Not only can this cause either red or blue shift, but the Doppler shift varies dynamically during a single communication event. So Doppler handling is an important feature in the modems used to process these communications.

• There is an interesting story about how the Huygens mission was doomed, because they had forgot to think about Doppler, as they found out during the 7 year voyage to Saturn! They saved the mission at the expense of some rocket fuel by optimizing the trajectory for minimum Doppler effect. – user2394284 Apr 20 '16 at 18:40
• @user2394284 wow, AWESOME read! – Magic Octopus Urn Sep 22 '18 at 0:19

Yes and no. You have to take into account the time dilation (as in GPS clocks). Maybe the comm equipment does allow for some minor frequency change and it just accepts it still working. However as the gravity does not change in linear fashion, I think the biggest changes will be in LEO/GO. You have to calculate the time speed difference between "there" and "here". For LEO or similar (GPS orbits) it's about ~38us per day. Diffrent time speed is visible in microwave radiation as redshift/blueshift. Not "speed" of the wave.

• I think I see where you are going with the answer but see events like thespacereview.com/article/306/1 which make some of your assertions questionable. If going down this line some maths on how time dilation would impact(or not) something like the equipment on the Parker solar probe would be interesting noting that it is not just clock time but the frequency of the radio equipment that will be impacted. – GremlinWranger Sep 22 '18 at 0:04