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Thread: keplers second law

  1. #1 keplers second law 
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    In proving keplers second law


    ds vector = small change in the position of the planet(say from A to B)

    x = angle between A and B

    r vector = the radius vector from o to B or A


    to prove dA/dt = constant where dA is the small area sweeped by the planet in small time dt through small distance ds

    we take dA = 1/2 *b*h = r x ds = r x (r dx) [ since s = rx]

    here we assume that AB(ds) is a straight line yet we replace ds by r dx...while r dx is applicable for a curve and for a curved line we cannot apply 1/2 b*h....
    my question is .....why cant we just continue the proof by taking dA = r x ds ?...why does ds needs to be replaced by r dx when ds is not a curve?


    sorry for my english....


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