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Semimajor Axis and Eccentricity after increased velocity 
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Jan2308, 07:58 PM

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Question:
A space shuttle is in an orbit about the Earth. At its apogee, it uses thrusters and increases its velocity by 400 m/sec. What is the new orbit semimajor axis, eccentricity and how much will the next perigee altitude be increased? Known: Original semimajor axis: 7000 km > a Original eccentricity: 0.05 > e Earth's Radius: 6378 km u= GxEarth's Mass=3.986x10[tex]^{5}[/tex] What I have done so far: I figured out the apogee and perigee of the orbit, as well as the velocity at the apogee before the firing of the thrusters. i) apogee: a(1+e) = 7350 km ii) perigee: a(1e) = 6650 km iii) velocity at apogee: [tex]\sqrt{u*((2/r)(1/a))}/[/tex] where r = apogee. I got v=7.17 km/s Now after the thrusters are fired, the new velocity is 7.57 km/s Using [tex]\epsilon[/tex] = V[tex]^{2}[/tex][tex]/2[/tex]  u[tex]/r[/tex] where r is the current position, aka the apogee and plugging [tex]\epsilon[/tex] into a = u[tex]/2\epsilon[/tex] I found the new semimajor axis to be 7809 km. But then here is the problem. How do I find out the new eccentricity? Thanks! 


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