Flat Earth Follies: Satellites would burn up in Thermosphere - Temperature vs Heat

Temperature vs Heat

"Satellites are allegedly floating around in the thermosphere where temperatures are claimed to be upwards of 4,530 degrees Fahrenheit. The metals used in satellites, however, such as aluminum, gold and titanium have melting points of 1,221, 1,948, and 3,034 degrees respectively, all far lower than they could possibly handle."- Eric Dubay

There is an excellent presentation on this done by ESA (Satellite Thermal Control) and many books on the subject (Spacecraft thermal control) -- I'm just going to look at one very basic property that will expose the absurdity of this claim.

Temperature is roughly a measurement of the average kinetic energy of some molecules, it say nothing about how many molecules there are or their ability to transfer that energy to another body. It should be obvious to anyone who thinks about it that 1 molecule at 1000°C is very different from ten septillion molecules at 1000°C.

Heat, on the other hand, is the amount of energy that flows from one mass to another. It is Heat that we really care about -- not merely temperature.

To put this difference into everyday terms, when you stick your hand into a 230°C/450°F oven it sure feels hot but you can dart your hand in, grab a piece of foil, and pull it out - all without burning yourself, but if you touch the metal sides you will get a burn very quickly.

It should be clear from this that Standard Dry Air, foil, and the metal used in the oven all have very different capacities to transfer Heat to your hand.

Other important properties are the emissivity and Thermal conductivity of both the Thermosphere and the satellite.  Satellite engineers care about such things in great detail which is why Satellites usually have some type of radiative cooling to dump waste heat (but it's mostly heat from the Sun and internal operations, not from the nearly non-existent atmosphere) and low thermal conductivity & reflective materials on the outside. (See more)

If we look at the energy required to raise 1 cm³ of Standard Dry Air to 273.15°K/0°C/32°F we find using Q=mc∆T that it's about 1/3 of a Joule (or about the energy required to lift 33 grams, 1 meter).  Our mass is about 0.001225 g and while specific heat of air varies, I used a generous 1.007 j/(gK).

That's how much energy would be available if you could somehow dump 100% of that energy into your satellite -- and that's if your satellite sitting in 0°C/32°F air.  In reality you could only dump a fraction of that into the satellite and the heating process would stop once they reach an equilibrium.

The ISS orbits at around 400 km, in the Thermosphere, where the temperature of molecules varies between about 740°K and 1350°K.  I'm going to use 1032.9°K for my example as that is the temperature the MSIS-E-90 Atmosphere Model gives for 400km at peak.

We also get a density of 4.883E-15 g/cm³ -- that's a mere 0.000000000000004883 grams!

The molecular density at these altitudes is VASTLY different from the density on the ground.  Since we just multiply all these numbers together you can see that even with 1350°K our energy is going to be very, very, very small.  Even with a generous value of c=2 j/(gK) we get 1.009×10⁻¹¹ J or one hundred billionth of a Joule.  That's 1/15th the mass-energy of just one proton.

Once you factor in the emissivity and conductivity factors (which lower the energy further), and take into account the exposed area and time (which would increase it) you still aren't anywhere near melting anything.

The density of surface air at 25°C is ~ 1.1839 kg/m³ compared to 0.000000000005 kg/m³ at 400km.  So that is about 2.5 x 10²⁵ molecules of air per m³ at the surface vs 10¹⁴ - so the temperature would have to be on the order of 10¹¹ degrees higher (not just 10²) for the heat transfer to be comparable between the two environments.  And once you hit the Exosphere we're talking about 900 MOLECULES per m³ -- by the time you are at geosynchronous orbits there are mere dozens of molecules, fewer by a factor of 10²⁵.

These are just rough estimates -- ignoring some of the physics as I said -- but the results are dominated by the extreme change in density, by many orders of magnitude.

The glaringly obvious conclusion is that while individual molecules in the Thermosphere are moving around pretty rapidly (high temperature), there just isn't enough of them to have enough energy to do a whole lot to a satellite.

They DO transfer some heat to the satellite and they DO slow down the orbit (proportional to their microscopic mass) but they do not melt anything.

Here is the chart of density and temperature: