Is space cold? Part 1

part 2

During Apollo 13 an explosion on the way to the moon damaged the service module, causing astronauts James Lovell, Jack Swigert, and Fred Haise to abort what would have been the third landing on the moon.  They came back to earth with the CM LEM and damaged SM.  The SM and LEM were jettisoned shortly before re-entering earth's atmosphere in the CM*.

Apollo configuration that went to the moon

The damaged service module was jettisoned shortly before returning to earth.

During this return journey, in the movie Apollo 13, the astronauts are portrayed as being cold.  

Apollo 13:  Houston are we supposed to be hot or cold here?  Houston:  Let me perform a calculation...(flips a coin).  OK according to the coin...er...calculation, you're supposed to be cold.  Act cold.

Without the damaged power systems to keep them warm the Apollo astronauts got cold because space is cold, right?  Actually, this cold state would be only be true if they were in the shadow of the earth or the moon.

The vast majority of the time, though, they were in the sun.  So they really should have been hot, not cold.

I thought it must be a movie error, that it was just Hollywood not getting their facts straight. Without their power systems working, rather than risk freezing, the astronauts would have cooked inside that aluminium can.  

Confident NASA would set the record straight, I went to their website only to find that NASA backs up the cold story of Apollo 13.  Someone at the time of Apollo 13 in 1970 must have made the erroneous cold claim and NASA has had to stick with the story ever since.  

The top of the command module had a shiny aluminium alloy exterior.  The SM was also mostly shiny with a black rocket nozzle.   

 Service module and command module

The LEM had various surfaces including gold coloured (multi-layer) metal foil, black paper, and beige paper.

AS11-40-5922.  NASA hi res version here.  Jack White's annotated version here.

AS14-66-9254.  NASA hi res version here.

A quick search of the internet shows the confusion NASA's Apollo 13 cold claim causes.  Many claim that the surface is reflective like a mirror, so it would have reflected most of the sun's light away.   

This is true, and this would keep it cooler than an object that has a higher absorptivity for a time; a white or a black object would heat up a lot quicker than a shiny metal one.  (This property was used in gold foil shields to protect Skylab, see below.)

But despite the high reflectivity of shiny metal, it has a low emissivity, and the surface still absorbs a small amount of EMR; while it will take longer than a duller surface to warm, the polished metal will reach a higher final temperature.

On earth, with an atmosphere to cool the surfaces, silver and white will be cooler than black.  A study on cars parked in the sun showed that black cars were hotter than silver or white ones.

In the vacuum of space, without an atmosphere to cool them, the roles are reversed.  Gold and silver will get hotter than black, while black is hotter than white.

Equilibrium temperature of a sphere in the sunlight from ground to space at a distance of earth's orbit.  On the ground black is hotter than metal.  In space shiny metal is the hottest colour.

Solar absorptivity of various substances.  Note how shape affects temperature as much as colour.

Polished metal has a high α/ε ratio and will get hot.  (Above three pictures from here.)

NASA admits that a metal will be hot in the sun stating:

When continuously orbiting the sun, some bare metals can reach temperatures above 260 degrees Celsius.

The International Space Station needs cooling when it is in the sun.  When the ISS is in the sun it turns its radiators at right angles to the sun's rays to dissipate heat and cool the station down.  During the night they turn the radiators to face earth in order to gather heat.

   

NASA's space station Skylab needed shielding from the sun and got hot when it lost its heat shield:

"The station was also heating up rapidly (temperatures approached [88C] at one point)"

Skylab

Skylab did use gold coloured foil shielding to protect it from the sun.  Given that an orbiting object spends half its time in the shade, and is only exposed to the sun for about 45 minutes at a time, a metal foil shield (with its low emissivity) could work.  

This shade was not available to the Apollo 13 astronauts during their return journey and the CM and LEM would have had no time to cool off.

If you still don't think the CM and LEM would get hot and need cooling, consider that the astronauts in the sun on the surface of the moon did need cooling. 

Even though the astronauts wore white, a colour that would be cooler in space than the metallic surfaces the space modules were covered in, NASA engineers had the foresight to design a cooling system for the astronaut's lunar excursions.

The porous plate sublimator provided about 1200W of cooling for the astronauts on the moon.

How could it be that when an astronaut is placed in the sun at the distance of earth's orbit they get hot and need cooling, and yet at the same time when the CM and LEM are in the sun they get cold? Obviously one of these points of view isn't true.  

Curious contradiction: NASA says the astronaut on the left needed cooling, while Apollo 13 on the right needed warming.

The claim of Apollo 13 being cold couldn't be true -- it would have gotten hot in the sun -- too hot for a human to survive without cooling.

....on to part 2.

* Corrected 3/7/2013: The SM was jettisoned shortly before returning to earth.