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From what I understand, an object has to keep moving in an orbit to not come crashing down to Earth. (The ISS is the first thing I think of for this.)

How then, do satellites which are purpose built for a particular region (satellite internet for example) stay in a fixed place?

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    $\begingroup$ They are put into a geosynchronous orbit.. This orbit is one in which the Earth rotates at the same angular velocity as the satellite.. $\endgroup$ – Andrew Thompson Feb 3 '16 at 5:09
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    $\begingroup$ So if the satellite slows down, they have to slow the earth down too $\endgroup$ – Reversed Engineer Feb 3 '16 at 15:02
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    $\begingroup$ If you were to say the satellites weren't actually moving, wouldn't that also suggest that the Earth isn't rotating? Otherwise the Earth would rotate away from the satellite :) $\endgroup$ – Broots Waymb Feb 3 '16 at 15:33
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Such satellites are in a geosynchronous orbit (GSO), orbiting at an orbital altitude where orbital period matches Earth's rotation on its axis. Their orbital speed is roughly 3 km/s at mean orbital altitude of 35,786 km above the Earth's surface:

  enter image description here

Orbital speeds ($v_o \approx \sqrt{\mu/r}$) at mean altitudes above the Earth's surface (blue) and required speed to keep up with Earth's rotation on its axis, aka the geosynchronous speed (green). Both speeds match at ~ 3,074 m/s at an altitude of ~ 35,783 km above the Earth's surface. Graph is first order approximation, real values are ever so slightly different.

Most commonly, communications satellites are placed in a geostationary orbit (GEO), which is a circular equatorial GSO, so the satellites stay roughly above the same longitude over the Earth's equator, while inclined circular GSO orbits produce a figure eight ground track, and highly eccentric inclined GSO like e.g. Tundra orbits produce an elongated figure eight. Note that some communications satellites might also operate in lower, non-geosynchronous orbits and depend on multiple satellites in constellations to assure constant coverage over specific regions on the Earth's surface, or globally.

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  • $\begingroup$ Thanks, I now realised I had the flawed assumption that the satellites rotated with Earth, but obviously that makes no sense! $\endgroup$ – Ricky Feb 3 '16 at 22:05
  • $\begingroup$ does the orbital altitude not also depend on the mass of the satellite? $\endgroup$ – Ricky Feb 3 '16 at 22:06
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    $\begingroup$ @Ricky Mass of an artificial satellite is many, many orders of magnitude smaller than the Earth and can be in this case neglected. Otherwise yes, for a circular orbit, orbital speed is $v_o \approx \sqrt{G (m_1 + m_2) / r}$ where $m_1$ and $m_2$ are the two masses (orbiting body and the one being orbited, tho that order can sometimes be ambiguous as e.g. with similar mass binaries). But if $m_1 + m_2 \approx m_2$, then it really doesn't matter. There are many other perturbing effects that will matter a whole lot more, such as perturbations of the Moon, solar pressure, mass concentrations,... $\endgroup$ – TildalWave Feb 3 '16 at 22:23
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It's important to pay close attention to your language when talking about matters involving reference frames. Communications satellites do not remain in a "fixed place" in the absolute sense, but they do "remain positioned above a particular region."

Since the Earth is rotating, if a satellite is in an orbit whose period is equal to one sidereal day, its movement will match the rotation of the Earth and it will remain positioned over the same location day in and day out. The orbit where this equivalency occurs is called Geostationary orbit (GEO) and is frequently the destination of communications and weather satellites.

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    $\begingroup$ Of course, it's only geostationary if it's over the equator (and prograde, strictly speaking) - otherwise it's just geosynchronous and covers the same set of points in each ~23.9 hours. AIUI many weather satellites are actually sun-synchronous (nearly-polar orbits that shift so that they're always over a given spot during the day). $\endgroup$ – Random832 Feb 3 '16 at 14:47
  • $\begingroup$ @Random832 (noting that you said many this doesn't change what you said) - the DSCOVR is at the Earth Sun L1 point... and nope, its not a communication satellite. $\endgroup$ – user5892 Feb 3 '16 at 15:06
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    $\begingroup$ Space weather is not the same thing as weather in the conventional sense. $\endgroup$ – Random832 Feb 3 '16 at 15:37
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    $\begingroup$ @Random832 " ... its not a communication satellite. ... " -> It's a "communications" satellite of sorts. What it's intending to communicate can be subtle, or seem so. It's a "pale blue dot reprise" satellite, or was, then was repurposed, then rerere..purposed to give it a raison d'etre, or an apparent one, and now it serves a different function than intended, while, arguably, still serving the same function as intended. Yes ? :-). $\endgroup$ – Russell McMahon Feb 4 '16 at 5:26
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    $\begingroup$ en.wikipedia.org/wiki/Deep_Space_Climate_Observatory $\endgroup$ – Russell McMahon Feb 4 '16 at 5:27

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