When Comet Holmes was heading away from Earth, we on Earth didn't see an angled view of the comet's tail. Was it tailless because of its motion? That is, would a comet also appear tailless if it were approaching, with Earth right in its path?
It's impossible to tell where a comet is heading based on the way its tail points. A dust tail is produced by microscopic dust particles released from the comet by the Sun's heat and driven away by sunlight (solar radiation pressure). So in 3-D space a comet's tail usually points away from the Sun, whether the comet is inbound or heading out.
This is why a comet low in the western evening sky at dusk (or low in the east before dawn) shows a tail extending generally upward, away from the Sun's location below your horizon.
— Roger W. Sinnott
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