are we moving with the aame speed both day and night with respect to sun
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We move around the sun in an elliptical orbit, so the line between the center of the sun and the center of the Earth swipes the same area in the same amount of time Δt . Since the orbit is almost circular, it is a good approximation to say we travel with constant speed around the sun.
Then you could have answered your own question with a bit of logical thinking: if it is light on one half of the earth (say Europe), it is dark on the other half (Australia, Japan). If speeds around the sun would differ for the light and dark sides, the Earth would be torn apart.
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