Arun
Last Activity: 5 Years ago
Let m1 and m2 be masses of satellites P1 and P2.
If M is mass of the earth, then
GMm1/R^2=m1v1^2/R OR
GM/R=v1^2 OR
v1=(GM/R)^1/2……..(1)
Similarly,for P2 satellite,
v2=(GM/4R)^1/2………..(2)
Then, linear velocity of P2 relative to P1 is v2-v1.
When both satellites will be nearest to each other,
angular velocity of the line joining them will be maximum. This maximum angular velocity will be
w( max)=(v2-v1)/3R= (GM)^1/2[ (1/4R)^1/2-(1/R)^1/2]/3R and for maximum distance of 5R between them
w(min.)=(GM)^1/2 [ (1/4R)^1/2-(1/R)^1/2]/5R. Then,
w(max)/w(min)=1/3R/(1/5R)=5/3