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A satellite revolves from east to west in a circular equatorial orbit of radius R=1.00*10^4km around the Earth. Find the velocity and the acceleration of the satellite in the reference frame fixed to the Earth. |
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Answer» Solution :The velocity of the SATELLITE in the inertial space fixed frame is `sqrt((gammaM)/(R))` east to west. With respect to the Earth fixed frame, from the `overset(rarr')v_1=vecv-(vecwxxvecr)` the velocity is `V^'=(2piR)/(T)+sqrt((gammaM)/(R))=7*03km//s` Here M is the mass of the earth and T is its period of rotation about its own axis. It would be `-(2piR)/(T)+sqrt((gammaM)/(R))`, if the satellite were moving from west to east. To find the acceleration we note the formula `moverset(rarr')w=VECF+2m(overset(rarr')vxxvecomega)+momega^2vecR` Here `vecF=-(gammaMm)/(R^3)VECR` and `overset(rarr')v_|_vecomega` and `overset(rarr')vxxvecomega` is directed towards the centre of the Earth. Thus `w^'=(gammaM)/(R^2)+2((2piR)/(T)+sqrt((gammaM)/(R)))(2pi)/(T)-((2pi)/(T))^2R` toward the earth's rotation axis `=(gammaM)/(R^2)+(2pi)/(T)[(2piR)/(T)+2sqrt((gammaM)/(R))]=4*94m//s^2` on substitution. |
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