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Show the nature of the following graph for a satellite orbiting the earth. (a) KE versus orbital radius R (b) PE versus orbital radius R (b) TE versus orbital radius R |
Answer» Solution :`implies` consider the diagram, where a satellite of mass m, moving around the earth in a circular ORBIT of radius R.  Orbital speed of the satellite orbiting the earth isgiven by `V_0=sqrt((GM)/R)` where, M and R are the mass and radius of the earth. (a) ` :.`KE of a satellite of mass m, `K=1/2 mv_0^2 =1/2 mxx(GM)/R` `:. K prop 1/R`  It means the KE decreases exponentially with radius. The graph for KE versus orbital radius R is shown in figure (b) Potential energy of a satellite. P.E. `=-(GMm)/R` `P.E. prop -1/R`  The graph for PE versus orbital radius R is shown in figure (c) Total energy of the satellite `E = K +U = (GMm)/(2R) - (GMm)/R` `=- (GMm)/(2R)`  The graph for total energy versus orbital radius R is shown in figure NOTE : We should keep in MIND that Potential energy (PE) and Kinetic Energy (KE) of the satellite-earth system is always NEGATIVE. |
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