The effective potential energy, E… | Physics

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The effective potential energy, E, of a lunar satellite of mass, m, moving in an. elliptical orbit around the moon of mass, m, is given by

\[ E = \frac{K^2}{2m_1r^2} - \frac{Gm_1m_2}{r} \] where r is the distance of the satellite from the mooń and G is the universal gravitational constant of dimensions, $M^{-1}L^3T^2$.

Ďetermine the dimensions of the angular momentum, K, of the satellite using dimensional analysis.

Answer

Dimensions of the angular momentum, K =

$\frac{[K]^{2}}{[m_{1}] [r]^{2}} = \frac{[G] [m_{1}] [m_{2}]}{[r]}$

$\frac{[k]^{2}}{M L^{2}} = \frac{M^{- 1} L^{3} T^{- 2} M^{2}}{L}$

[K] = (M $^{2}$ L4T $^{- 2}$ )½

$∴$ [k] = ML $^{2} T^{- 1}$

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Answer Details

Dimensions of the angular momentum, K =

$\frac{[K]^{2}}{[m_{1}] [r]^{2}} = \frac{[G] [m_{1}] [m_{2}]}{[r]}$

$\frac{[k]^{2}}{M L^{2}} = \frac{M^{- 1} L^{3} T^{- 2} M^{2}}{L}$

[K] = (M $^{2}$ L4T $^{- 2}$ )½

$∴$ [k] = ML $^{2} T^{- 1}$

Read lesson note on Gravitational Field (JAMB)

Gravitational Field

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The effective potential energy, E, of a lunar satellite of mass, m, moving in an. elliptical orbit around the moon of mass, m, is given by \[ E = \frac{K^2}...

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The effective potential energy, E, of a lunar satellite of mass, m, moving in an. elliptical orbit around the moon of mass, m, is given by \[ E = \frac{K^2}...

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