Although there is a question similar to this, this is a variation that I am pret

Question

Although there is a question similar to this, this is a variation that I am pretty confused about how to solve.

One way to attack a satellite in Earth orbit is to launch a swarm of pellets in the same orbit as the satellite but in the opposite direction. Suppose a satellite is in a circular orbit 500 km above the Earth’s surface. What would be the speed of such a pellet relative to the satellite? What is the ratio of this relative speed to the speed of a bullet fired from a military rifle (3110 feet per second for an M-16)?

Explanation / Answer

Speed of satellite at 500 km above earth's surface= v = sqrrot ( GMe/r)

G = gravtational constant= 6.67 x 10^-11 N m^2/kg^2, Me = mass of earth = 5.98 x 10^24 kg

r = Re +R

Re = radius of earth = 6.38 x 10^6 m

R = 500 km = 5 x 10^ 5 m

v= sqrrot [( 6.67 x 10^-11 x 5.98 x 10^24)/ ( 6.38 x 10^6 + 0.5 x 10^6) ] = 7.614 x 10^3 m/s apprx

As the pellets are travelleing oppsite to satellite, their speed must be equal to satellite to bring it to sto

Speed of pelletts with respect to speed of satellite = - 7.614 x 10^3 - ( +7.614 x 10^3) = - 15.228 x 10^3m/s apprx

b) Ratio of relative speed / speed of bullet

converting 3110 feet per second to m/s = 947.928 m/s

ratio = 15.228 x 10^3/ 947.928= 16.06 apprx

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