What is the ratio of the gravitational force that Earth exerts on the Sun in the

Question

What is the ratio of the gravitational force that Earth exerts on the Sun in the winter and the force that it exerts in the summer in the Northern Hemisphere? Hint: Earth's orbit is an ellipse with the Sun located at one of the foci of the ellipse. The Earth is approximately 1.473×1011m from the Sun when it is winter in Northern Hemisphere, and 1.521×1011m when it is summer. What is the ratio of the speed of the Earth moving around the Sun when it is winter in Northern Hemisphere to this speed in summer.What is the ratio of the gravitational force that Earth exerts on the Sun in the winter and the force that it exerts in the summer in the Southern Hemisphere?

Explanation / Answer

Fwinter / Fsummer =(GmeMs/R12)/GmeMs/R22=R22/R12 =(1.521*1011)2/(1.473*1011)2 =1.066235

V=(GM/R)1/2

Vwinter /Vsummer =(R2/R1)1/2 =(1.521/1.473)1/2=1.016

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