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The speed at the perihelion is 30.28km/s and aphelion speed is 29.3km/s. It is calculated by using Newtons equation combined with a few others in circular motion. Using the distance from the sun at the two points and the equation F=GMm/r^2 we can work out the force the sun exerts on the earth. With that we can use F=mv^2/r to work out the v. We could combine the equations to make it slightly easier and we would get v=sqrt(GM/r) where G is the gravitational constant (6.67x10^-11) and M is the mass of the sun (1.99x10^30 kg)
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Why physics and technology depended on each other