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Suppose one wanted to modulate the power of a hypothetical, powerful ion thruster on the ISS to continuously compensate the atmospheric drag force in order to achieve near-perfect free-fall conditions (near-zero microgravity) for the station's experiments, at least between other maneuvers.

What is the time dependence of the drag force on the ISS? Is it fairly constant, say within 10% over a given orbit? Or is there a large day/night variation due to interaction of solar radiation and solar wind with the ionosphere?

Are there other effects that can cause significant changes in drag force on the ISS within the timeframe of a given orbit as well?

note: This is a Gedankenexperiment to explore the nature of the drag force on the ISS at its orbital altitude, not a proposal for a practical way to minimize microgravity, as there are several other considerations, so there's no need to start a list of these in comments. This question has its origins from comments below this answer.

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  • $\begingroup$ Remember Tiangong-1? Even the day before they changed the predicted time of impact to serval hours later because of lack of expected solar activity. So it sounds like there is a pretty significant amount of variation, though I don't have any numbers. $\endgroup$ – Nathanael Vetters Apr 10 '18 at 12:25
  • $\begingroup$ @NathanaelVetters the strong feedback in atmospheric reentry makes the problem much more unpredictable. At 400 km the ISS only looses about 10 meters or less per orbit, so that kind of exponential behavior isn't really a good model here. $\endgroup$ – uhoh Apr 10 '18 at 12:52
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    $\begingroup$ Not enough for a true Answer, but perhaps it’ll help somebody: there’s a significant difference in atmospheric density (at 100’s of km altitude) with latitude. That would be a twice-per-orbit effect. It also has a day-night difference. The only non-pay walled paper I have handy is Newton&Pelz: agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JA074i016p04169 $\endgroup$ – Bob Jacobsen Apr 10 '18 at 13:47
  • $\begingroup$ Oops, sorry, looks like that paper actually is paywalled. My mistake. I’ll see what I can find... $\endgroup$ – Bob Jacobsen Apr 10 '18 at 13:52
  • $\begingroup$ @BobJacobsen it's available from NASA. Although data from Explorer in 1966 may not be the final word on the subject, it certainly is interesting to read about! $\endgroup$ – uhoh Apr 10 '18 at 14:43
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In this presentation about Satellite Drag there is a table with the density variations in a orbit height of 400 km.

The solar cycle causes variations of 1600 % and a period of 11 years.
Semianual variations with 125 % and a period of 12 months.
Solar rotation (UV radiation) with 250 % and a period of 27 days.
Major geomagnetic storms with 800 % and 3 days.
Diurnal (day/night) effect with 250 % and a period of 1 day.

The Thermosphere is heated by the Sun, the density increases on the day side of Earth. The ISS will experience a density modulation within an orbit's period of about 90 minutes.

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    $\begingroup$ This! The huge variations in drag over the eleven year solar makes predicting drag very hard, and a bit of a fiction. The large (but not quite huge) variation over the short term makes predicting the day on which a satellite will reenter so hard. One good solar flare, which can happen even in weak solar cycles (e.g., the Carrington Event), can make the Earth's atmosphere swell up like an overheated marshmallow. $\endgroup$ – David Hammen Apr 11 '18 at 1:31
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    $\begingroup$ @David Hammen: A cite from the presentation: "During the great geomagnetic storm of 13-14 March 1989, tracking of thousands of space objects was lost. One LEO satellite lost over 30 kilometers of altitude, and hence significant lifetime, during this storm." $\endgroup$ – Uwe Apr 11 '18 at 8:03
  • $\begingroup$ Yikes! What a beautiful, interesting mess! $\endgroup$ – uhoh Apr 11 '18 at 10:23
  • $\begingroup$ @Uwe Has NORAD ever experienced a catastrophic event and "lost" a bunch of satellites? $\endgroup$ – uhoh Apr 11 '18 at 10:32
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Take a look at this paper on how well Gravity Probe B did exactly that. It has plots of the required countering acceleration as a function of the time scale (expressed in frequency). GP-B was in a higher orbit, 642 km, but variability should be similar in time, just much less in magnitude.

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  • $\begingroup$ We normally warn new users about link-only answers, so to be fair I should do it here as well. Can you include at least a summary or screen shot of the countering acceleration as a function of time scale (figure 9?) in order to preserve some of the value and utility of your answer if/once the link rots? Thanks! $\endgroup$ – uhoh Apr 11 '18 at 1:53
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    $\begingroup$ Also see upload.wikimedia.org/wikipedia/commons/e/e5/ISS_altitude.png , which shows ISS altitude over a period of a bit over seven years. Once well past the peak of solar cycle 23, the ISS was allowed to operate at altitudes that would have been hazardous during the peak of that solar cycle. $\endgroup$ – David Hammen Apr 11 '18 at 2:08
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Orbit : Apogee : 408 km Perigee : 401.1 km

Kepler law of equal area in equal time says that the velocity ratio Apogee/Perigee = 6808/6801.1 km = 1.001

Drag is propertional to square of velocity hence drag ratio = 1.002

Assumption : Drag coefficient is same for the velocities and atmospheric density does not change appreciably in 7 km difference at such high altitude.

So, 0.2% should be the change in drag force.

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  • $\begingroup$ Oh that is so ignorant of me. I’ll edit the answer. $\endgroup$ – Prakhar Apr 10 '18 at 14:38
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    $\begingroup$ Variation in altitude will add a proportionality factor, which should not be significant. I will look for equation valid for LEO density variation $\endgroup$ – Prakhar Apr 10 '18 at 14:51
  • $\begingroup$ This answer misses the large diurnal effect (a factor of more than two), the much larger variations due to smallish changes in solar activity, and the absolutely huge variations over the course of the eleven year solar cycle. $\endgroup$ – David Hammen Apr 11 '18 at 1:34
  • $\begingroup$ Diurnal effect happens because if you are at perigee and it is night at perigee point, because of much cooler temperature the density will decrease at LEO? Or increase? $\endgroup$ – Prakhar Apr 11 '18 at 2:35
  • $\begingroup$ The diurnal effect has nothing to do with spacecraft altitude variations. It is a variation in the atmosphere itself. The Sun heats up the sunlit side of the Earth's atmosphere, making it swell up. The atmosphere on the unlit side of the Earth cools and shrinks. The ISS sails through this large variation in density about 16 times a day. $\endgroup$ – David Hammen Apr 11 '18 at 11:44

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