The exosphere is almost a vacuum. This picture shows the Hubble Space Telescope orbiting Earth in the exosphere. Places that are lit by sunlight are very hot. Places in the shade are very cold.
Click on image for full size
Image courtesy NASA.
Temperature in the Exosphere
The exosphere is almost a vacuum. The "air" is very, very thin there. When air is thin, it doesn't transfer much heat to objects in the air, even if the air is very, very hot.
One definition scientists use for temperature is the average speed of the molecules or atoms in a gas. When the particles are moving very fast, the temperature is hot. When particles are bouncing around more slowly, the temperature is cooler. The particles in the exosphere are moving very quickly, so the temperature there is quite hot. However, the exosphere would feel quite cold to us. How can that be? Since the "air" is so thin in the exosphere - it is almost a vacuum - there are very, very few particles. We feel warmth when particles hit our skin and transfer heat energy to us. There are too few particles in the exosphere to transfer much energy, even though each particle is quite "hot" itself.
Objects in the exosphere are hot if lots of sunlight shines on them. Sunlight is very, very bright up there, so objects in the sunshine heat up quickly. However, objects in the shade can get really, really cold. For example, one side (the sunny side) of a satellite might be very hot, while the other side (in the shade) might be freezing cold.
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