Do other planets experience total solar eclipse like the one we witnessed on July 22, 2009?

They don’t – and given the orbital dynamics of the planetary bodies, they never will. Total solar eclipses occur only on Earth, thanks to a remarkable coincidence. In essence, this involves two factors: Size and distance. The Sun and the Moon are apparently the same size in the sky, a fact that is hard to see for oneself, since the Sun should never be viewed directly. Rather than the actual size, it is this apparent size that matters and makes possible one of the most spectacular and awe-inspiring events in the natural world – the total solar eclipse, when the Moon’s disk almost perfectly covers the entire body of the Sun.
Two numbers are important in understanding this lucky relationship of size and distance: 400 and 108. The Sun has a diameter about 400 times that of the Moon; at the same time the Sun is about 400 times farther away from the Earth than the Moon. Both the Sun and the Moon are about 108 times their own diameters away from the viewer. No other planet and its natural satellites have the kind of relationship which the Earth and the Moon have with the Sun.

The maximum possible duration of an eclipse of the Sun is 7 minutes 40 seconds. However, from a supersonic Concorde aircraft traveling at the same speed as the moving shadow of the Moon (1,673 kilometers/hour) astronauts have observed it for 3.5 hours.

Additional Reading:
Solar eclipse (Wikipedia)

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