Question

Problem 3: You and your friend are both starship captains. Your friend is orbiting a planet in a circular orbit at an altitude of 2 x 10 m above the surface. Your ship is also in a circular orbit but is at an altitude of 7 x 10 m above the surface. (Mplanet = 2 x 1023 k¥ and Rplanet = 4 x 106 m) a) [4 points] What are the orbital speeds of the two ships in their circular orbits? Diagram for parts B&C b) [6 points] By what amount would you need to alter your velocity to drop your orbit down so that it touches your friend's orbit as shown in the diagram to the right? Would this be an increase Your Friend с or decrease in velocity?

Answer 1

23 Ans:) tadius of faiend's orbit = Rp = 6x10m radius of my orbit = Rm = 11x 10 m Mpeanet Ripianet 4x10cm Rs and Rm are measured from the centre 2x10 kg of the planet 10 Let me be the mass of friend's ship orbital G Mesanet me speed of. Rif Ps friend's ship. FG Metanet => Vf me v Vf Ff 6.673 X10' x 2X1023 6 X10 2-1092 x 10 ms.

similarly orbital speed of my ship is Vm Vm = GM planet 6673X10"*2*1033 Rm + * to 1.10149 X 10 mis b) To drop down to friend's oibit my abital speed should change from 10149x 10 mu to 2.1092x 10 ms. change in Apeed require is 1.00771 X 100 m It would be an increase in the velocity, at point c' the radius of curvature of the two orbits are same hence my speed at c equals friend's speed in his orbit je. 2.1092x10' mla e)

Moon r 2 Planet d) M moon 6 x 1022 kg d = 4 x 107m let v be the escape relocity at c. My kinetic energy at 'C' = potential energy at c =-G Mmoon Mm Mm mais Gi Mpianet Mm ship, RE since v is the escape velocity hence total energy at 'e' is zero i.e. 2 Mmv²_ G Minoan Mm GM planet Mm - RG r of my r

V = a = la Gi Mmoon 7/2 GMpeanet 7 신 2 = 2x6,672x10" 6 X1022 4x107 + 2x1023 6x10C v 2156.1207 45 m/s