Editing Doppler effect (section)

===Satellites===
{|style="margin: 0 auto;"
| [[File:SatDoppler.png|thumb|300px|upright|Possible Doppler shifts in dependence of the elevation angle ([[Low Earth orbit|LEO]]: orbit altitude <math>h</math> = 750&nbsp;km). Fixed ground station.<ref>Otilia Popescuy, Jason S. Harrisz and Dimitrie C. Popescuz, Designing the Communica- tion Sub-System for Nanosatellite CubeSat Missions: Operational and Implementation Perspectives, 2016, IEEE</ref>]]
| [[File:DopplerSatScheme.png|thumb|300px|upright|Geometry for Doppler effects. Variables: <math>\vec{v}_\text{mob}</math> is the velocity of the mobile station, <math>\vec{v}_\text{Sat}</math> is the velocity of the satellite, <math>\vec{v}_\text{rel,sat}</math> is the relative velocity of the satellite, <math>\phi</math> is the elevation angle of the satellite and <math>\theta</math> is the driving direction with respect to the satellite.]]
| [[File:SatDopplerSpectrum.png|thumb|300px|upright|Doppler effect on the mobile channel. Variables: <math>f_c = \frac{c}{\lambda_{\rm c}}</math> is the carrier frequency, <math>f_{\rm D,max}=\frac{v_{\rm mob}}{\lambda_{\rm c}}</math> is the maximum Doppler shift due to the mobile station moving (see [[Rayleigh fading#Doppler power spectral density|Doppler Spread]]) and <math>f_{\rm D,Sat}</math> is the additional Doppler shift due to the satellite moving.]] 
|}

====Satellite navigation====
{{main|Satellite navigation}}
The Doppler shift can be exploited for [[satellite navigation]] such as in [[Transit (satellite)|Transit]] and [[DORIS (satellite system)|DORIS]].

====Satellite communication====
{{main|Satellite communication}}
Doppler also needs to be compensated in [[satellite communication]]. 
Fast moving satellites can have a Doppler shift of dozens of kilohertz relative to a ground station. The speed, thus magnitude of Doppler effect, changes due to earth curvature. Dynamic Doppler compensation, where the frequency of a signal is changed progressively during transmission, is used so the satellite receives a constant frequency signal.<ref>{{Cite book|last=Qingchong |first=Liu |title=MILCOM 1999. IEEE Military Communications. Conference Proceedings (Cat. No.99CH36341) |chapter=Doppler measurement and compensation in mobile satellite communications systems |volume=1 |year=1999 |pages=316–320 |doi=10.1109/milcom.1999.822695|isbn=978-0-7803-5538-5 |citeseerx=10.1.1.674.3987 |s2cid=12586746 }}</ref> After realizing that the Doppler shift had not been considered before launch of the [[Huygens (spacecraft)#Critical design flaw partially resolved|Huygens probe]] of the 2005 [[Cassini–Huygens]] mission, the probe trajectory was altered to approach [[Titan (moon)|Titan]] in such a way that its transmissions traveled perpendicular to its direction of motion relative to Cassini, greatly reducing the Doppler shift.<ref name="TitanCalling">{{cite news|title=Titan Calling |first=James |last=Oberg |publisher=[[IEEE Spectrum]] |url=https://spectrum.ieee.org/aerospace/space-flight/titan-calling |archive-url=https://archive.today/20120914080503/http://spectrum.ieee.org/aerospace/space-flight/titan-calling |url-status=dead |archive-date=September 14, 2012 |date=October 4, 2004 }} (offline as of 2006-10-14, see [https://web.archive.org/web/20041010192803/http://www.spectrum.ieee.org/WEBONLY/publicfeature/oct04/1004titan.html Internet Archive version])</ref>

Doppler shift of the direct path can be estimated by the following formula:<ref>Arndt, D. (2015). On Channel Modelling for Land Mobile Satellite Reception (Doctoral dissertation).</ref>
<math display="block">f_{\rm D, dir} = \frac{v_{\rm mob}}{\lambda_{\rm c}}\cos\phi \cos\theta</math>
where <math>v_\text{mob}</math> is the speed of the mobile station, <math>\lambda_{\rm c}</math> is the wavelength of the carrier, <math>\phi</math> is the elevation angle of the satellite and <math>\theta</math> is the driving direction with respect to the satellite.

The additional Doppler shift due to the satellite moving can be described as:
<math display="block">f_{\rm D,sat} = \frac{v_{\rm rel,sat}}{\lambda_{\rm c}}</math>
where <math>v_{\rm rel,sat}</math> is the relative speed of the satellite.