Find an approximate solution for the time variation of r

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Reference no: EM131383088

A satellite of mass m moves under the attractive inverse square field -(mγ /r²)r^{^} and is also subject to the linear resistance force -mKv, where K is a positive constant. Show that the governing equations of motion can be reduced to the form

r^·· + Kr^· + (γ/r²) - (L₀²e^-2Kt/r³) = 0,

r²θ^· = L₀e^-Kt,

where L₀ is a constant which will be assumed to be positive. Suppose now that the effect of resistance is slight and that the satellite is executing a ‘circular' orbit of slowly changing radius.

By neglecting the terms in r and r, find an approximate solution for the time variation of r and θ in such an orbit. Deduce that small resistance causes the circular orbit to contract slowly, but that the satellite speeds up!

Reference no: EM131383088

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