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"There are two forces that counter the negligible centripetal force. 1. Earth's Gravitational force 2. Countering force of atmosphere carried with the earth The rate of change of centripetal force is very very small in centripetal forces if you consider a complete loop and the mammoth distance the earth covers in an year."
so, is gravity (earth gravity acceleration for us) on the night is less than at day ?
Gravity comes from mass. The more mass an object has, the more gravity it will exert on objects around it. The amount of gravity that you experience falls off quickly over distance. So, the force of gravity that you feel on the surface of the Earth is much different from what you would experience at the distance of the Moon, or further. 9.8 m/s2 is the gravity close to the surface. You might be surprised to know that the force of gravity on Earth actually changes depending on where you’re standing on it. The first reason is because the Earth is rotating. This rotation is trying to spin you off into space, but don’t worry, this force isn’t much. The gravity of Earth at the equator is 9.789 m/s2, while the force of gravity at the poles is 9.832 m/s2. In other words, you weigh more at the poles than you do at the equator because of this centripetal force.
This needs to be cleared up... the reason we don't feel the sun's gravity is the same reason that astronauts in the international space station feel weightless -- because we're in free fall around the sun. The sun's gravity is certainly not negligible, it's what keeps us in orbit. But since the earth is accelerating with us, we don't feel it. Secondly, if you're being REALLY strict about it, we would weigh ever so slightly more at night because the sun and the earth are pulling us in the same direction. The earth's pull is far greater than the sun's, so this effect is not noticeable.