This depends on the beta angle, which is the angle between the plane of the orbit and a vector to the Sun. If the orbit appears face-on to the Sun the beta angle is 90 degrees and there is no obscuration of the Sun as seen from the ISS. If the orbit appears edge on to the Sun the beta angle is 0 degrees and the Sun will be obscured for a maximum amount of time.

Betas for the ISS vary from 0 degrees to a maximum of 75.1 degrees, i.e. the Earth’s obliquity of 23.5 degrees plus the ISS’s orbital inclination of 51.6 degrees. The ISS orbits at an average altitude of about 370 km, thus its orbital period is about 92 minutes. When beta is equal to zero the ISS spends about 36 minutes in shade and 56 minutes in sunlight. When beta is at its maximum of 75.1 degrees the ISS will never move into shade, though the conditions have to be just right for this to happen and are probably rare.

Hopefully I didn't mess up my math in calculating the above. I know someone who is an ISS flight controller; I'll check with him to verify this correct.

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I'd have to do some digging, but I know the ISS goes through "sunshine marathons" maybe a couple of times a year, where it is in constant sunlight for several days. (I'm thinking during the solstices, or thereabouts).

Bob,

Your numbers are right on.

One minor nit; the beta angle ranges from -75 to + 75. But I know what you were trying to say.

Good, it’s nice to get confirmation. Regarding the beta angle, I forgot to mention it is measured as a positive or negative number depending on which face of the orbit is visible to the Sun. When calculating the length of time the ISS is in the shadow of the Earth, it doesn’t matter whether the angle is positive or negative.

It definitely has to happen near the solstices because that is when Earth’s axis is most directed toward the Sun, however there is more to it than that. For maximum beta to occur the ascending node of the ISS orbit has to be located so that the inclination of the orbital plane is in the same direction as the Earth’s axial tilt. The longitude of the ascending node has a precession rate of sometime like –5 degrees/day, so the orbit won’t always be inclined in the direction needed to produce a maximum, or near maximum, beta angle.

EDIT:

If I did my math right, it looks like the precession cycle of the ISS orbit is about 71 days. It appears then that at sometime within approximately a month either side of a solstice, the ascending node will be such that a large beta angle will be achieved. The minimum beta angle needed to produce a condition in which the ISS never moves into shade is about 71 degrees (or –71 degrees). Without getting into some messy geometry I can’t say whether an angle this large will be achieved near every solstice, but it certainly seems there will be a brief period of time in which the ISS is in continual or near continual sunlight once every six months or so.

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It does seem to be a particular (though not unique) trait of "HBs" or "CTs" that they see refutations of their ideas as personal attacks.

Jay, didn't you do some research into the psychology of HBs/CTs? We have a software engineer here who does the same thing. I evaluated a processing method he devised and determined it was not workable for the specific project I was working on, and he took it as a personal attack, to the point of e-mailing the program manager (who tried to put me over a barrel). If I can get an insight into the HB/CT mind, it might help me deal with him better.

CJSF

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Two years ago moved from my town
I was looking up past the city lights
But the city lights got in my way

See the constellation ride across the sky
No cigar, no lady on his arm
Just a guy made of dots and lines

-from "See The Constellation"
by They Might Be Giants

Tread carefully. Not all manifestations of ego protection are equivalent.

In the conspiracy theorist's case, the theory is a part of a fantasy world erected to protect the ego from a universe that does not give the conspiracist the attention he believes he deserves. The degree to which he chooses to interact with and through the fantasy world would probably be the degree to which a psychiatrist might diagnose a mental illness.

But anyone in a creative profession is susceptible to having too much emotional stake in his ideas. It takes a lot of experience to learn to have enough pride in your work to drive it, but not so much that you can't let go of an idea that objectively won't fly. Technical skill and emotional maturity usually vary independently, and the latter is important when working with people. But in my opinion, that's an example of normal ego protection that does not qualitatively match the delusional world of conspiracism.

In an employment context, it's best to take the de minimis approach. Don't assume your coworker's reaction is anything more than a genuine misunderstanding of the reasons for which you passed on his idea. I would choose, for example, to emphasize that it appears to be a well-considered piece of technology, but it simply doesn't fit the problem you're trying to solve. Instead of saying, "Your software doesn't do this or that," say, "The problem would require software that can do this or that."

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Clavius Moon Base

Thanks, Jay. That helps clear up a few questions, and points me in some new (and better) directions to look.

CJSF

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Two years ago moved from my town
I was looking up past the city lights
But the city lights got in my way

See the constellation ride across the sky
No cigar, no lady on his arm
Just a guy made of dots and lines

-from "See The Constellation"
by They Might Be Giants

I only happened on this thread today and found it fascinating and illuminating. I had the following thought as I sludged along: A goggle search on "earth temperature without greenhouse effect" will lead to multiple posts that say, in effect, 'without the greenhouse effect the earth would be at a temperature at or somewhat below the freezing point of water'. I expected this because the usual college level Astronomy Intro text is likely to show the same info in a table. Why, I wonder, did/does it seem strange that a spacecraft at the same distance from the sun might have a similar equilibrium temperature when power disapating devices have been shut down? I know that it does not mean that this must be the Apollo 13 condition, but simplicity suggests that it does mean it could be the Apollo 13 condition.

One thing that several people tried to point out to IDW is that the Earth as a whole exchanges energy with the rest of the Universe solely (well, close enough) by radiation. The Earth is just a big wet spaceship without a hull. And it's had billions of years to come to equilibrium. So why hasn't it heated up to unsustainable levels? (Come to think of it, even the worst predictions for global warming don't mean that the planet will become uninhabitable.)

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I always find the analytical-comparative dichotomy interesting. An analytical approach taxonomizes on the basis of the discovered root causes of behavior. A comparative approach taxonomizes on the basis of observed behavior itself. Practical investigation requires elements of both, but conspiracy theorists never seem to get the hang of choosing the approach.

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Clavius Moon Base

And if you look at Earth from outside and measure its radiation budget, it looks like an object that is (on average) below freezing. It has to, because of the aforementioned equilibrium. It's the complexity of Earth's internal workings that allow it to sustain an average surface temperature higher than freezing, by ensuring that some of its surface-radiated photons don't get straight back out to space.
The analogy with a powered-down spacecraft, which has its own internal complexity, seems pretty clear.

Grant Hutchison

?? Now I know how those Gieco Caveman feel.

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--Bender

I tried to explain this exact thing to IDW at GLP a couple years ago. His response was, "but the Earth has an atmosphere and magnetic field". Rather than argue that point, I change my example to the Moon, which has neither an atmosphere nor magnetic field, yet is in thermal equilibrium at a global temperature close to freezing point of water. As best as I can recall, he ignored me an changed the subject.

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Since IDW has been banned and probably isn't actually reading this forum anymore, I can finally reveal the truth.

The Apollo spacecraft was cooled with freeze-dried ice cream.

As promised I asked my ISS flight controller friend about this and here is what he said (quoted with permission):

It's nice to know someone on the inside who can give us the straight dope.

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You know it always amazes me that HBs can't understand that you can insulate an cool a spacecraft, but they will quite happily take their food out of a freezer set to about -5°C and place it in an oven set to 200°C, both of which are in the same room, and hardly blink.

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Howling from the Shadows

It must be fun to lead a life completely unburdened by reality. --- JayUtah

You can't reason an irrational person out of an irrational belief. --- Noclevername

Apollo: The History and the Hoax
Enter the World of Athran

Great job, Bob et al.! I really think it's important to recognize that there are people whose job it currently is to build and fly actual spacecraft. It's not an exotic science-fiction scenario. These people are as dedicated, diligent, and competent at their jobs as any in any other job, and face a variety of problems every day ranging from the mundane to the mind-boggling, just like everyone else. Keeping a spacecraft warm or cool is simply a thing that people do in the normal courses of their employment, much as others evaluate loan requests, others repair sprinkler systems, others cook food, and others care for the elderly.

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"Facts are stubborn things." --John Adams
Clavius Moon Base

*gasp*

But what about the... and the... oh booger.

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You know it always amazes me that HBs can't understand that you can insulate an cool a spacecraft...

Yes, people often misunderstand what it means to insulate something thermally. It means heat doesn't transfer across that boundary. Why is that rocket science.

Heat transfer is filled with counterintuitive concepts. When I was a teenager first learning about heat transfer, I wondered how in the world a car engine could be cooled on a hot day, ca. 100 F outside. I couldn't imagine there was enough cooling capacity in air that hot. But when you run the numbers and you look at auto coolant at 200 F and air at 100 F, you realize there's plenty of thermal gradient still left to exploit. 100 F air at 70 miles per hour can achieve a surprising degree of forced convection cooling of 200 F coolant. Engineers can exploit even narrow differences in temperature. The human body intuitively considers both 100 F and 200 F as "hot." But cooling needs only a difference in temperature, not any absolute.

My favorite counterintuition example is the considerable danger involved in putting one's hand in 140 F water, while we can reach with relative impunity into a 450 F oven. The difference there is the density of the convection medium. Many variables affect heat transfer, often in drastic magnitudes. Intuition is almost always wrong.

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Clavius Moon Base

Thanks, Bob! Excellent information. So, we know that the ISS (and other manned craft that have been in high inclination orbits, such as the Shuttle and many Russian craft) have to deal with both full sunlight at times and a nearby planet. If you can design for that, you can design for the conditions Apollo faced.

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Disclaimer: Avatar is not an official NASA image and does not imply any specific interplanetary or interstellar capability.

The Leif Ericson Cruiser

Yep, we got some excellent material out of this thread. Jay, and others, provided some really good and interesting information about Apollo's thermal control systems and strategies. We've further learned the ISS, and other Earth orbiting spacecraft, go through periods when they are subjected to thermal conditions more severe than Apollo had to endure while traveling to and from the Moon. The next time this Apollo cooling argument comes up we should all be well prepared to refute it.

One further note: All Russian/Soviet spacecraft have to launch into high inclination orbits because of the location of their launch site. This means the old Salyut spacestations, first launched in 1971, also had to deal with these high beta conditions. Therefore an HB can't argue that it is some sort of newfangled modern technology that allows the ISS to survive. The technology had to exist back in Apollo's day and both the Americans and Soviets had it.

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For anyone with the inclination to learn about heat transfer there is a free textbook available here as a pdf file from a local (Houston) engineering professor and public radio show host and his son. It is probably not space related but anyone that takes the time to understand this material should no longer have doubts about the science involved.

A Heat Transfer Textbook, 3rd edition
John H. Lienhard IV, Professor, University of Houston
John H. Lienhard V, Professor, Massachusetts Institute of Technology
Copyright (c) 2000-2006, John H. Lienhard IV and John H. Lienhard V. All rights reserved.

This book is an introduction to heat and mass transfer oriented toward engineering students. It may be downloaded without charge.

Revised versions are posted regularly; the version number is given on the titlepage verso. Visit this page again to obtain updates.

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I encounter one of those examples quite often. I have a French press for brewing coffee, and have found placing it in a 170 deg. F oven it keeps the unused coffee at just the right temperature for drinking without "burning" it. Obviously, after some time the entire press and the rack it sits on are all about 170 F. I can reach in and take the press out by its rubber-covered handle without a problem, but I can't touch the oven racks or the metal or glass parts of the press. A nice demonstration of the effect of differing thermal conductivities, without having to walk over hot coals.

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"Slapping a guy on the head is just as funny now as it was eighty years ago."

Not to dog pile on, but...

I just remembered when they lost contact with SOHO early in the mission. One of the first things mission managers had to do after regaining contact was re-orient the satellite to thaw out the frozen hydrazine fuel lines. Hydrazine freezes at 1 degree C or so. SOHO was at L1 (or orbiting L1) at the time of LOS, and L1 is closer to the sun than the moon ever gets, right?

Nice example, shame IDW has been banned so he can't reply (like he would anyway).

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"Any Sufficiently Analyzed Magic is Indistinguishable from SCIENCE!" -Agatha Heterodyne

"Any technology, no matter how primitive, is magic to those who don't understand it." -Florence Ambrose

And we must also consider Skylab, the counterexample.

The loss of the combined heat and micrometeoroid shield during the ascent caused hot internal temperatures. The heat shield provided mechanical protection from debris and meteor strikes and optical protection from excessive absorption and radiation.

The shield comprised a number of panels with appropriate optical coatings to absorp, reflect, and radiate as needed in that part of the structure. Absorptivities likely ranged from 0.10 to 0.15 for the most reflective parts, and emissivities up to 0.85. The underlying skin was plated with gold alloy. It had been designed to interact thermally with the shield through absorption and radiation; it was not in direct contact with it. The gold skin roughly reverses those optical properties: absorption between 0.20 and 0.25 and emission at 0.03.

That made Skylab effectively a greenhouse; it would absorb a great deal of solar energy and radiate very little. The designed skin would have absorbed comparatively little energy (except where specially provided) and emitted well.

The damaged Skylab cannot be considered similar to an Apollo spacecraft in terms of the optical properties that affect heat transfer and eventual cabin temperature. They are as different as they can be.

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"Facts are stubborn things." --John Adams
Clavius Moon Base

"They are as different as they can be." Totally differant missions. One was a trans-lunar shuttle for short term use and the other an orbital habitat and lab for long duration occupancy.

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"If they put me on a postage stamp tell them to use the young Bender"
--Bender

Nice to see this thread is back up - it's providing some illuminating discussion of radiative thermodynamics, even if the original poster wasn't as interested in learning.

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Speaking of radiators...

Current events: STS-118 shuttle astronauts do something to the ISS P6 radiator described as "P6 forward radiator retraction" in the flight plan:





These are helmet-cam shots. Both show the camera-wearer's hands for scale, and the second shows a distant astronaut. The P6 radiator is the structure of parallel plates towards the top of each shot.

Edit: In briefing, operation was described as packing (I think) radiator in preparation for a move in a subsequent mission. That might not be its normal deployed appearance.

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0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...

And notice the beta angle value on the ground-track display, in the upper left.

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