The velocity of Satellite A is 2% greater than velocity of satellite B.
The given parameters;
The forces acting on the Satellites are given as follows;
[tex]F_c = \frac{mv^2}{r} \\\\F_g = \frac{GMm}{r^2} \\\\\frac{v^2}{r} = \frac{GM}{r^2}\\\\v^2 = \frac{GM}{r} \\\\v^2 r = GM\\\\v_1^2 r _1 = v_2^2 r_2\\\\v_A^2r_A = v_B^2 r_B\\\\(\frac{v_A}{v_B} )^2 = \frac{r_B}{r_A} \\\\\frac{v_A}{v_B} = \sqrt{\frac{r_B}{r_A} } \\\\\frac{v_A}{v_B} = \sqrt{\frac{(800,000\ + \ 6.4 \times 10^6}{(500,000\ + \ 6.4 \times 10^6} )} \\\\\frac{v_A}{v_B} = 1.02 \\\\v_A = 1.02 \ v_B[/tex]
[tex]v_A = v_B( 100\% \ + 2\%)\\\\v_A = 100\%v_B \ + \ \ 2\% v_B\\\\v_A = v_B \ \ + \ 2\% v_B[/tex]
Thus, the velocity of Satellite A is 2% greater than velocity of satellite B.
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