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Physics

Mechanics

Easy

Question

A satellite revolves in elliptical orbit around a planet of mass M. Its time period is T and M is at the centre of the path. The length of the major axis of the path is: (neglect the gravitational effect of other objects in space)

$2 {[\frac{G M T^{2}}{4 π^{2}}]}^{1 / 3}$
${[\frac{G M T^{2}}{4 π^{2}}]}^{1 / 3}$
$\frac{1}{2} {[\frac{G M T^{2}}{4 π^{2}}]}^{1 / 3}$
None

The correct answer is: $2 open square brackets fraction numerator G M T squared over denominator 4 pi squared end fraction close square brackets to the power of 1 divided by 3 end exponent$

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell 1 colon fraction numerator m v squared over denominator r end fraction equals square root of fraction numerator G M over denominator r squared end fraction end root m end cell row cell text Also end text T equals fraction numerator 2 pi r over denominator v end fraction equals fraction numerator 2 pi r to the power of 3 divided by 2 end exponent over denominator square root of G M end root end fraction not stretchy rightwards double arrow T squared equals fraction numerator 4 pi squared r cubed over denominator G M end fraction end cell end table table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell not stretchy rightwards double arrow space of 1em r equals open parentheses fraction numerator G M T squared over denominator 4 pi squared end fraction close parentheses to the power of 1 divided by 3 end exponent equals text Radius end text end cell row cell not stretchy rightwards double arrow text Diameter (major axis) end text equals 2 open parentheses fraction numerator G M T squared over denominator 4 pi squared end fraction close parentheses to the power of 1 divided by 3 end exponent end cell end table$

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