How Spacecraft Survive Extreme Temperature Swings

Without thermal control, NASA-attributed figures put a sunlit surface on the International Space Station near 250°F (121°C) and a shadowed one near minus 250°F (minus 157°C), and the station circles Earth every 90 minutes. No spacecraft survives that by accident. Here is how spacecraft survive extreme temperature swings: how a vacuum changes the physics of heat, the toolkit of coatings, insulation, radiators, and heaters, and how the ISS, the James Webb Space Telescope, and the Parker Solar Probe each solve a different version of the same problem.

Why space is hot and cold at the same time

On Earth, heat moves three ways. Conduction passes it through direct contact, convection carries it in moving air or liquid, and radiation sends it across empty space as infrared light. A hot stove cools faster near an open window because moving air strips heat from the surface. Most of everyday life leans on convection without our noticing.

In the vacuum around a spacecraft, convection is gone. NASA's spacesuit designers put it bluntly in a 2017 briefing: there are two ways to transfer heat in space, conduction between touching objects and radiation. That leaves a spacecraft thermally isolated in a way nothing on Earth's surface ever is. It cannot dump heat into passing air, and it cannot borrow warmth from it either. Conduction still works inside any structure, and why some materials pull heat away from your hand faster than others is the subject of our explainer on why metal feels colder than wood. Every surface settles at whatever temperature its own energy budget dictates.

That energy budget is the heart of spacecraft thermal engineering. NASA's SmallSat thermal chapter writes it as a single balance: the heat arriving from the Sun, the heat reflected from a planet's surface (albedo), the heat radiated by the planet itself (planetshine), and the heat generated by onboard electronics must equal the heat stored in the spacecraft plus the heat radiated away. Think of a bathtub. Sunlight, albedo, planetshine, and electronics are four taps running into the tub; radiation to space is the drain; the water level is the temperature. A spacecraft is in trouble when the taps and the drain stop matching for too long.

A campfire is a good picture of how uneven the result can be. Face it and your front is hot while your back is cold, because radiation only warms the side that can see the fire. A satellite works the same way, with the Sun as the fire and deep space as the cold night behind it. Surfaces facing the Sun, Earth, or open space each end up at different temperatures, with no air to blend them. Sunlight also pushes as well as heats, a separate effect that solar sails turn into propulsion.

Where the famous numbers come from, and why they disagree

Several figures circulate for how hot and cold it gets. Discover Magazine, citing NASA figures in a 2010 article about a failed cooling loop, reported that without thermal controls the sun-facing side of the station would reach about 250°F (121°C) and the shadowed side about minus 250°F (minus 157°C). ESA gives a range of about 120 degrees in direct sunlight to minus 160 in shadow, without naming the unit. A NASA briefing from spacesuit engineers gives minus 150°F to plus 250°F for objects in low Earth orbit.

These numbers do not describe the same thing. The Discover figure is explicitly a case without thermal controls. The others describe ranges for objects or spacewalkers rather than readings from a thermometer on a particular panel. A surface's real temperature depends on its coating, what it faces, and how long it has been in sun or shade, so any single pair of numbers is a bounding case. The takeaway for the rest of this article is to treat "hundreds of degrees" as a design problem, not as a measurement.

The orbit sets the tempo. NASA's station facts page says the ISS makes 16 orbits of Earth in 24 hours, passing through 16 sunrises and sunsets, completing an orbit roughly every 90 minutes at about five miles per second. A cold shadow or a hot Sun arrives every 45 minutes or so, a rhythm that gives a large structure little time to settle and engineers no chance to ignore.

A worked example: why radiators have to be so big

Radiation is slow, and it gets weaker quickly as a surface cools. The Stefan-Boltzmann law says the power radiated per square meter of an ideal surface equals a constant times the fourth power of its absolute temperature. NIST lists the constant as 5.670374419 × 10⁻⁸ watts per square meter per kelvin to the fourth power. Real radiator coatings fall short of the ideal, and the fraction they achieve is called emissivity.

The arithmetic below is illustrative. It assumes one radiating face, an emissivity of 0.85, and ignores sunlight and planetshine falling on the panel.

Radiator temperature	Ideal radiation (W/m²)	At emissivity 0.85 (W/m²)	Area to reject 1 kW (m²)
300 K (27°C)	459	390	2.6
250 K (-23°C)	221	188	5.3

Cooling the radiator from 300 K to 250 K, a drop of about 17 percent in absolute temperature, cuts its output to 48 percent, so the area needed more than doubles. That fourth-power penalty is why engineers want radiators as warm as the electronics allow, and it is one reason heat-rejection panels are such large structures on big spacecraft like the ISS.

A real example shows the scale. NASA's overview of the station's active thermal control system describes the Photovoltaic Radiator, which can reject up to 14 kilowatts of heat into deep space and measures 3.12 meters by 13.6 meters when deployed. That is roughly 42 square meters of panel footprint for 14 kilowatts, or about 330 watts per square meter of footprint, in the same range as the idealized figures above.

The toolkit

Spacecraft thermal engineers do not rely on one clever material. They combine a handful of tools, each handling a different part of the budget, and then verify the result in a vacuum chamber. NASA's JPL summarizes the passive tools as insulating blankets, optical solar reflectors, paint, and shading, and the active tools as heaters, louvers, and radioisotope heater units.

Tool	What it controls	How it works	Example with numbers
Coatings and finishes	How much sunlight a surface absorbs and how well it radiates	Matches absorptivity and emissivity to the job	Optical solar reflector tile, solar absorptivity about 0.08 at start of life
Multi-layer insulation (MLI)	Heat flow through the skin	Stacked reflective films separated by gaps	Typically 10 to 20 reflective layers plus an outer protective layer
Radiators	Rejecting internal heat	High-emissivity panels radiate infrared into space	ISS photovoltaic radiator, up to 14 kW
Heaters, louvers, heater units	Keeping parts above their minimum temperature	Thermostat-controlled resistive heaters, bimetallic shutters, radioisotope sources	Polyimide (Kapton) heaters listed at roughly 0.02 to 7.75 W/cm² depending on product
Heat pipes, straps, phase-change materials	Moving or buffering heat inside	Fluid, graphite, or melting material carries or stores heat	Paraffin melts between 20 and 60°C, absorbing 140 to 280 kJ/kg

Sources: NASA SmallSat Institute thermal control chapter; NASA JPL Basics of Space Flight.

Coatings: absorb little, radiate well

Every surface has two properties that matter. Solar absorptivity is the fraction of sunlight it soaks up; emissivity is how efficiently it radiates infrared. A radiator wants low absorptivity and high emissivity, so it sheds heat without collecting any. NASA's SmallSat chapter describes white paint and silver-coated fluorinated tape as having exactly that combination, while black paint has high absorptivity and high emissivity.

This produces a counterintuitive habit. JPL notes that internal components are often painted black so they radiate heat to each other and to the structure more efficiently, while the outside is white, gold, or mirrored. The inside of a spacecraft is a heat-sharing environment, and the outside is a heat-rejecting one.

The numbers are small but decisive. NASA's SmallSat chapter gives beginning-of-life solar absorptivity of 0.08 for a quartz optical solar reflector, 0.07 to 0.08 for certain silvered films, and 0.10 to 0.14 for silver and aluminum composites on one grade of Kapton. It adds that coatings darken over time from atomic oxygen in low Earth orbit and from ultraviolet light and cosmic rays at higher altitudes, raising absorptivity, so engineers use beginning-of-life values for cold cases and end-of-life values for hot cases. A design that is comfortable at launch can overheat in year ten.

Multi-layer insulation: a stack of mirrors, not a blanket

Multi-layer insulation is the gold or silver foil visible on many spacecraft. NASA's SmallSat chapter says it typically has 10 to 20 reflective layers with an outer protective layer, and that perforations or edge venting let trapped gas escape. Performance drops sharply when the layers are compressed, because contact creates a conductive short, and edge effects hurt small spacecraft the most.

It works like a thermos. Each thin film reflects infrared back toward where it came from, and the gaps between films stop conduction, so heat has to cross the stack one reflection at a time. JPL explains the gold color: it comes from a silvery aluminum coating behind amber Kapton sheets. The blankets reflect infrared to limit solar heating and also retain internal heat, so the same material keeps a cold instrument from warming and a warm one from cooling.

Heaters, louvers, and radioisotope sources

On the cold side, the simplest tool is also the most common: a resistive heater. JPL describes autonomous thermostatically controlled heaters and heaters that ground controllers can switch on or off. NASA's SmallSat chapter lists electrical heaters as highly mature in low Earth orbit and notes that several small CubeSats used battery heaters during eclipses.

Louvers add a clever twist. JPL explains that louver blades change angle to vary the effective emission of the surface beneath them, opened by bimetallic strips similar to a thermostat's. When the inside is hot the blades open and the surface radiates; when it is cold they close. Louvers can reduce the heater power a spacecraft needs, which matters because every watt spent on heat is a watt not available for science. For deep-space missions, radioisotope heater units placed at specific locations provide warmth without drawing any power from the main bus.

Heat pipes, straps, and melting wax

Moving heat inside a spacecraft is its own problem. NASA's SmallSat chapter describes thermal straps, flexible links that conduct heat from a source to a sink without adding structural load, and heat pipes, sealed tubes whose internal wicks return fluid to the hot end so it can evaporate again. Phase-change materials work like a thermal capacitor. Paraffin, for example, melts between 20 and 60°C and absorbs 140 to 280 kilojoules per kilogram while it does, which smooths out short bursts of heat from electronics or the sudden change when a spacecraft enters eclipse.

The same logic shows up in everyday devices. Our explainer on why thermal throttling slows devices covers what happens when a chip's heat has nowhere to go, and on Earth it is solved with fans that a spacecraft cannot use. For another system built around moving heat with a pumped fluid, see how heat pumps move heat efficiently.

The International Space Station: a floating power plant with plumbing

The ISS is the largest thermal problem in orbit. Its eight solar arrays provide 75 to 90 kilowatts, according to NASA, and nearly all of that electrical energy ends up as heat in the station's electronics. A Boeing-authored NASA overview of the Active Thermal Control System describes a mechanically pumped fluid loop that collects, transports, and rejects waste heat when the station's passive thermal control cannot cope on its own.

The system has two halves for a safety reason. Inside the pressurized modules, the loops use water, which the overview describes as efficient and safe in a habitable module. Outside, the External Active Thermal Control System uses anhydrous ammonia, which has an extremely low freezing point of minus 107°F (minus 77°C) and a wide operating range. Interface heat exchangers pass heat from the water to the ammonia, and they are mounted outside the pressurized volume because ammonia is highly toxic. Each exchanger core has 45 alternating layers, with water flowing through 23 and ammonia through 22 in the opposite direction.

The external system has two independent loops, one on the starboard side and one on the port side. It is designed to reject 35 kilowatts per loop for a total of 70 kilowatts, according to NASA's overview, and it serves all the U.S. and international partner modules except the Russian ones. The two loops are physically separated so orbital debris cannot take out both, and the fluid lines are buried in the truss structure. If one loop fails, the system operates at reduced capacity.

Inside, two water loops handle different temperature needs. The Low Temperature Loop is designed to operate near 40°F (4°C) and cools systems such as the cabin air assembly, while the Moderate Temperature Loop runs near 63°F (17°C) and covers most avionics and payload experiments. The overview gives their fluid volumes as about 63 liters and about 200 liters, and says the loops can be run as a single loop to reduce pump wear or work around a pump failure. The water side is a cousin of the crew's life-support water, which our article on how astronauts recycle water in space covers separately.

Two details show how much of this is control, not just plumbing. The external radiators constantly rotate to optimize cooling as the station moves, driven by a thermal radiator rotary joint. And heaters are wrapped around the ammonia lines to prevent freezing during periods of low heat load, switched on and off by software or by plain thermostats with no software interface at all.

Failures are instructive. In the August 2010 incident that Discover Magazine covered, a tripped circuit breaker took down one of the ammonia loops, and NASA planned two spacewalks to replace the Pump Module, which circulates the coolant. The crew was never in danger, but the episode showed why the station has two loops rather than one. Our overview of the International Space Station puts these systems in the context of the whole outpost.

The James Webb Space Telescope: five umbrellas facing the Sun

Webb has the opposite problem. Its infrared instruments need to be extremely cold so that the telescope's own warmth does not drown the faint light it is collecting. NASA states that most infrared detectors need about 40 kelvin (minus 233°C, or minus 388°F), and the instrument that observes mid-infrared light, MIRI, needs even more: a cryocooler brings its first stage to 18 K and its detectors to 7 K.

The solution is a sunshield roughly the size of a tennis court, according to Physics World, made of five layers of Kapton film. The first layer is 0.05 millimeter thick and layers two through five are 0.025 millimeter, each coated with about 100 nanometers of aluminum. The sun-facing sides of the two hottest layers carry an additional doped-silicon coating about 50 nanometers thick, and NASA says the doping makes it conductive so the membranes can be grounded and avoid static buildup.

The geometry matters as much as the materials. NASA says the layers do not touch, so heat cannot conduct from one to the next, and their shape and spacing direct heat from the spacecraft out through the gaps at the edges. Think of five beach umbrellas stacked above one another, each open at its sides: heat that gets through the top one escapes sideways instead of leaking down to the next. NASA says the fifth layer mostly adds margin against imperfections and micrometeoroid holes. The membranes are sized so the mirrors see only the coldest layer while the Sun shines only on the first.

Two sets of temperatures, and what they mean

Before launch, Physics World reported expected temperatures of 383 K for the outermost layer and about 36 K for the innermost. That is a difference of 347 kelvin across a few meters of film. NASA's current explainer rounds the picture differently, giving a hot side of up to 358 K (85°C) and a cold side of about 40 K (minus 233°C). Both agree on the point that matters: the sunshield separates a warm side facing the Sun from a cold side facing deep space, and the cold side meets the instruments' requirement.

Quantity	Value	Source type
Sun-facing layer, pre-launch expectation	383 K (about 230°F)	Physics World report
Coldest layer, pre-launch expectation	about 36 K	Physics World report
Hot side, current NASA explainer	up to 358 K (85°C)	NASA science explainer
Cold side, current NASA explainer	about 40 K (minus 233°C)	NASA science explainer
Position	Sun-Earth L2, 1.5 million km from Earth	NASA

Webb works at the Sun-Earth L2 point, about 1.5 million kilometers from Earth, so its thermal design is built around one steady Sun-facing shield rather than the rapid day-night cycle of low Earth orbit. Our explanations of how Lagrange points hold space telescopes and how space telescopes see in infrared cover why that location and that wavelength go together, and our Webb overview covers what the telescope has found.

Surviving damage and proving it on the ground

Large thin films tear, so Webb's engineers designed for it. Physics World reports that seams and rip-stops limit tears to about 1 by 2 meters, and sunshield manager James Cooper of NASA Goddard said that "we can meet performance requirements with this size tear in any layer." NASA adds that thermal spot bonds melt the layers together at points and reinforcing strips are bonded about every 6 feet, forming a grid of rip-stops. Each corner has a membrane tensioning system with 15 cables, 90 in all, and unfurling begins three days after launch and takes five days.

The proof that it works came from a vacuum chamber. According to AmericaSpace, Webb underwent 93 straight days of around-the-clock thermal vacuum testing at NASA's Johnson Space Center in Houston, ending when the chamber door was unsealed on November 18, 2017. The chamber's door is 40 feet in diameter and weighs 40 tons. The test simulated 40 kelvin and was the first time the telescope's optics and instruments were tested together. Our explainer on why vacuum chambers are useful in science covers the technique more broadly.

The Parker Solar Probe: a heat shield that keeps instruments at room temperature

If Webb is about staying cold, Parker is about staying cool next to a star. NASA's Goddard Space Flight Center describes its heat shield as two panels of carbon-carbon composite sandwiching a carbon foam core 4.5 inches (11.4 centimeters) thick, about 8 feet (2.4 meters) in diameter and roughly 160 pounds (73 kilograms). The Sun-facing side is sprayed with a white coating formulated to reflect solar energy away.

At closest approach, NASA reports the shield's outer surface reaches nearly 2,500°F (about 1,370°C) while instruments in the shield's shadow stay near 85°F (29°C). That is a difference of about 1,340 Celsius degrees across a few inches of foam. On December 24, 2024, Parker flew within about 3.83 million miles (6.2 million kilometers) of the Sun's surface at roughly 430,000 miles per hour, according to NASA. NASA's pre-launch description of the mission had put its closest approaches at about 4 million miles (6.4 million kilometers), so the December 2024 pass went closer than the original design figure.

The foam is the quiet hero. A carbon foam core conducts little heat, so the outer face can glow while the inner face stays comparatively mild, a bit like the thick insulation in an oven door. For the mission itself, see our overview of the Parker Solar Probe.

JPL describes an earlier answer to the same problem. MESSENGER's ceramic-cloth sunshade kept the spacecraft at room temperature despite sunlight about 11 times more intense than at Earth, and its solar panels were 70 percent optical solar reflectors and 30 percent solar cells. Our article on Mercury covers the planet it studied.

The cold side: Mars rovers and heat you already have

Not every mission fights the Sun. Rovers on Mars and probes at Jupiter and Saturn fight the cold, and they often do it with heat that would otherwise be waste. NASA's technical summary for the Mars Science Laboratory describes a mechanically pumped fluid loop that recovers waste heat from the rover's radioisotope power source and delivers it to the electronics when it is cold, then reverses to reject heat to the environment when it is warm. The loops circulate a Freon (CFC-11) fluid, and heat exchangers around the power source use aluminum facesheets and aerogel insulation so one side can run hot while the other stays cool.

That architecture is a good reminder that spacecraft thermal control is mostly about heat that is already there. For rovers, see our article on the Perseverance and Curiosity rovers, which share this approach in broad terms. JPL's guide notes that active cooling by refrigeration is generally impractical on interplanetary spacecraft, so the heat has to go somewhere simple: into a radiator, or into the next job.

Planets matter too. A spacecraft near one absorbs not only sunlight but also reflected light and the planet's own infrared glow, which is why the energy balance above includes both albedo and planetshine. Our explainer on why Venus is hotter than Mercury covers the planetary side of that heat.

When thermal control fails: Skylab and cold batteries

The clearest failure in spaceflight history was a thermal one. Skylab launched on May 14, 1973, and a design flaw let air get under the micrometeoroid shield, which peeled away during launch. Without it, the Smithsonian's National Air and Space Museum reports, temperatures inside Skylab rose over 130°F (about 54°C) and reached about 150°F (about 66°C) in places.

The fix was a sunshade. Engineer Jack Kinzler of Johnson Space Center proposed a parasol with aluminum poles and fabric of nylon, Mylar, and aluminum, deployed through an 8-inch instrument port so no spacewalk was needed. After the first crew installed it, the temperature dropped to a livable 90°F (about 32°C). The first crew, Pete Conrad, Paul Weitz, and Joseph Kerwin, slept in their command module at first because Skylab was still too hot, and on June 7, 1973, Conrad and Kerwin freed a jammed solar panel on a spacewalk. A "twin pole" sunshade installed by the second crew later replaced the parasol. The lesson is that a spacecraft's temperature depends on a single outer layer remaining in place.

Batteries show the opposite lesson. Lithium-ion cells do not like to be charged cold. A JPL-led paper on the Mars InSight lander's battery says engineers had to charge and discharge from minus 30°C to plus 35°C, a wider range than earlier Mars landers required, and worried that lithium could plate onto the anode during low-temperature charging and degrade performance. They solved it with a JPL-developed low-temperature electrolyte. Our explainers on how lithium-ion batteries work and on why lithium-ion batteries age cover the chemistry behind that constraint.

Placement is itself a thermal tool, because it decides which parts see the extremes at all, and NASA's SmallSat chapter notes that several 1U CubeSats carried battery heaters specifically for eclipse periods.

Common misconceptions about spacecraft and temperature

"Space is cold, so it freezes spacecraft instantly." Space has no temperature in the way air does, because there is almost nothing there to carry heat. A spacecraft loses heat to space only by radiating it, and radiation is slow. That is why heaters and insulation have time to work. A shadowed surface cools gradually, on a timescale set by its mass and coating.

"The shiny foil is decoration." The gold and silver blankets are engineered insulation, with layer counts, perforations, and coatings chosen for each mission. JPL notes that gold is used to shade critical components. Compressing or damaging the layers degrades performance sharply, so the foil is hardware, not packaging.

"Spacecraft just need to stay cool." Many need to stay warm. Batteries, propellant lines, and optics all have minimum temperatures, and the ISS's ammonia loops carry heaters specifically to prevent freezing. Thermal control is about keeping every part inside its own window, and the windows differ by hundreds of degrees between a battery and an infrared detector.

"Thermal design is finished at launch." It is not. Coatings darken, heaters cycle, and orientation changes. Thermal engineers watch temperature sensors throughout the spacecraft and command heaters or recommend operational changes to keep limits from being violated, a process JPL describes as continuing through the mission.

FAQ

Q: Why do spacecraft face such extreme temperature swings? A: In a vacuum there is no air to carry heat, so a surface warms only by absorbing radiation and cools only by emitting it. A sunlit surface and a shadowed surface can therefore differ by hundreds of degrees. NASA-attributed figures for the ISS without thermal control are about 250°F (121°C) in sunlight and about minus 250°F (minus 157°C) in shadow.

Q: What is multi-layer insulation, and why is it gold? A: Multi-layer insulation is a stack of typically 10 to 20 thin reflective layers with gaps between them, which blocks conduction and reflects infrared. JPL explains the gold color comes from a silvery aluminum coating behind amber Kapton sheets.

Q: How do spacecraft avoid overheating from their own electronics? A: They carry the heat to radiators, panels with high emissivity that radiate infrared into space. On the ISS, pumped ammonia loops move heat from the interface heat exchangers to external radiators, and the system is designed to reject up to 70 kilowatts.

Q: What happens when a spacecraft enters a planet's shadow? A: Its surfaces lose heat by radiation and cool over time, and thermostat-controlled heaters keep sensitive parts such as batteries above their minimum temperature. Phase-change materials and thermal mass smooth the transition.

Q: How does the Parker Solar Probe survive so close to the Sun? A: A heat shield made of carbon-carbon composite panels around a 4.5-inch carbon foam core faces the Sun, reaching nearly 2,500°F (about 1,370°C) on its outer surface, while the instruments behind it stay near 85°F (29°C), according to NASA.

Q: Why does the James Webb Space Telescope have five sunshield layers? A: The layers do not touch, so heat cannot conduct from one to the next, and their shape directs heat out through the edges. NASA says five layers block enough heat with margin, with the fifth adding protection against imperfections and micrometeoroid holes.

Q: Can a thermal failure end a mission? A: It can cripple one. Skylab's interior rose above 130°F (54°C) after its micrometeoroid shield was lost in 1973, until a parasol sunshade brought it down to about 90°F (32°C). Most spacecraft add redundant heaters and sensors for this reason.

The takeaway

Spacecraft do not survive temperature extremes through a single clever material. They survive by managing one energy budget with several imperfect tools: coatings that choose what to absorb, blankets that slow heat, radiators that let it go, heaters that add it back, and fluid loops that move it around. The ISS rejects tens of kilowatts through ammonia plumbing, Webb isolates a 40-kelvin telescope behind five layers of film each about as thin as a human hair, and Parker holds its instruments near room temperature a few inches from a 2,500°F shield. The common thread is that heat in a vacuum has only two ways to travel, and every design is a way of choosing which one to allow.

Sources

• NASA, "Space Station Facts and Figures"
• NASA/Boeing, "Active Thermal Control System (ATCS) Overview" (ISS)
• NASA SmallSat Institute, State-of-the-Art Small Spacecraft Technology: Thermal Control
• NASA JPL, Basics of Space Flight, Chapter 11: Spacecraft thermal control
• NASA Science, "How does Webb stay cold?"
• NASA, "The Complex Material Engineering of NASA's Webb Telescope Sunshield"
• NASA Science, "Sunshield membrane coatings" (Webb)
• Physics World, "The ten billion dollar gamble: how the JWST shields itself from the Sun"
• AmericaSpace, "Final deep freeze thermal vacuum testing wraps up on James Webb Space Telescope" (November 28, 2017)
• NASA Goddard, "Cutting-edge heat shield installed on NASA's Parker Solar Probe"
• NASA Science, "A Big Year for Our Sun" (Parker Solar Probe December 2024 perihelion)
• NASA Technical Reports Server, Mars Science Laboratory heat rejection and recovery system (NPO-47619)
• Smithsonian National Air and Space Museum, "Saving Skylab"
• Discover Magazine, "ISS astronauts plan emergency spacewalk to fix the station's AC"
• ESA, "EVA: Not exactly a walk in space"
• NASA Technical Reports Server, "Why Does it Look Like That? The Story of Space Suit Design" (2017)
• JPL/ECS, "The Use of Low Temperature Lithium-Ion Batteries to Enable the NASA InSight Mission on Mars"
• NIST, CODATA value of the Stefan-Boltzmann constant

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