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Kirchhoff's law is only valid for objects in thermal equilibrium. The emissivity and absorptivity of a material are the same for a given wavelength, but can vary dramatically for different wavelengths.

The radiators on a spacecraft are not in thermal equilibrium, since they are emitting heat. They emit heat in the longwave infrared spectrum, but receive heat energy (from the Sun) in the shortwave infrared, visible, and UV parts of the spectrum. This means that the effective emissivity and absorptivity can differ while the radiators are in operation.

The radiators on the ISS are a high-emissivity white paint, meaning that they are dark in the infrared spectrum where the heat is emitted. They are white in the visible spectrum to reflect sunlight.

The radiators on the shuttle are have a two-layer coating: a silver reflective layer covered by a thin Teflon film. The Teflon layer is opaque to infrared light, so the high emissivity of Teflon dominates. Visible light passes through the Teflon layer and is reflected by the silver layer, so the solar absorbance is low.

The radiators on the Shuttle are exposed to more direct sunlight (the radiators on the ISS pivot so they are typically close to edge-on to the Sun), which is why they use the higher-performance but more expensive dual-layer design.

Kirchhoff's law is only valid for objects in radiative equilibrium. The emissivity and absorptivity of a material are the same for a given wavelength, but can vary dramatically for different wavelengths.

The radiators on a spacecraft are not in radiative equilibrium, since they lose heat to radiation. They emit heat in the longwave infrared spectrum, but receive heat energy (from the Sun) in the shortwave infrared, visible, and UV parts of the spectrum. (They do also receive longwave IR from Earth, but the amount is only around 250 W/m² vs 1300 W/m² for sunlight.) This means that the effective emissivity and absorptivity can differ while the radiators are in operation.

The radiators on the ISS are a high-emissivity white paint, meaning that they are dark in the infrared spectrum where the heat is emitted. They are white in the visible spectrum to reflect sunlight.

The radiators on the shuttle are have a two-layer coating: a silver reflective layer covered by a thin Teflon film. The Teflon layer is opaque to infrared light, so the high emissivity of Teflon dominates. Visible light passes through the Teflon layer and is reflected by the silver layer, so the solar absorbance is low.

The radiators on the Shuttle are exposed to more direct sunlight (the radiators on the ISS pivot so they are typically close to edge-on to the Sun), which is why they use the higher-performance but more expensive dual-layer design.

The radiators on the ISS are a high-emissivity white paint, meaning that they are dark in the infrared spectrum where the heat is emitted. They are white in the visible spectrum to reflect sunlight.

The radiators on the shuttle are have a two-layer coating: a silver reflective layer covered by a thin Teflon film. The Teflon layer is opaque to infrared light, so the high emissivity of Teflon dominates. Visible light passes through the Teflon layer and is reflected by the silver layer, so the solar absorbance is low.

The radiators on the Shuttle are exposed to more direct sunlight (the radiators on the ISS pivot so they are typically close to edge-on to the Sun), which is why they use the higher-performance but more expensive dual-layer design.

Kirchhoff's law is only valid for objects in thermal equilibrium. The emissivity and absorptivity of a material are the same for a given wavelength, but can vary dramatically for different wavelengths.

The radiators on a spacecraft are not in thermal equilibrium, since they are emitting heat. They emit heat in the longwave infrared spectrum, but receive heat energy (from the Sun) in the shortwave infrared, visible, and UV parts of the spectrum. This means that the effective emissivity and absorptivity can differ while the radiators are in operation.

The radiators on the ISS are a high-emissivity white paint, meaning that they are dark in the infrared spectrum where the heat is emitted. They are white in the visible spectrum to reflect sunlight.

The radiators on the shuttle are have a two-layer coating: a silver reflective layer covered by a thin Teflon film. The Teflon layer is opaque to infrared light, so the high emissivity of Teflon dominates. Visible light passes through the Teflon layer and is reflected by the silver layer, so the solar absorbance is low.

The radiators on the Shuttle are exposed to more direct sunlight (the radiators on the ISS pivot so they are typically close to edge-on to the Sun), which is why they use the higher-performance but more expensive dual-layer design.

According to this document:

Light colors are good emitters of radiation. For example, the radiators on the ISS are white, which helps them to emit their radiant energy.

Wikipedia tells us that both black and white paint have high emissivity. As GdD said in the comments, it is likely that they choose white paint to minimize heat absorption.

The radiators on the ISS are a high-emissivity white paint, meaning that they are dark in the infrared spectrum where the heat is emitted. They are white in the visible spectrum to reflect sunlight.

The radiators on the shuttle are have a two-layer coating: a silver reflective layer covered by a thin Teflon film. The Teflon layer is opaque to infrared light, so the high emissivity of Teflon dominates. Visible light passes through the Teflon layer and is reflected by the silver layer, so the solar absorbance is low.

The radiators on the Shuttle are exposed to more direct sunlight (the radiators on the ISS pivot so they are typically close to edge-on to the Sun), which is why they use the higher-performance but more expensive dual-layer design.