This photo, taken by the IMAGE satellite, shows the upper atmosphere (plasmasphere) trailing off into space for several thousand miles. The round ball is the Earth, and the bright ring is the aurora oval above the North Pole.
Very roughly, the 'edge of space' starts about 100 kilometers above the Earth, but there is still part of the Earth's atmosphere even at this altitude. The atmosphere just gets less and less dense. At these altitudes, the 'scale height' is several hundred kilometers, so that means the continued decrease in the atmosphere slows down significantly. Even at 1000 kilometers, there is a trace of the Earth's 'hydrogen cloud' as its outer atmosphere.
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