ADVANCED MECHANICS I
ADVANCED MECHANICS I PHYS 302
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This 1 page Study Guide was uploaded by Miss Elbert Nader on Wednesday October 21, 2015. The Study Guide belongs to PHYS 302 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/225908/phys-302-texas-a-m-university in Physics 2 at Texas A&M University.
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Date Created: 10/21/15
Physics 302 Pre test chapter 8 A spacecraft is in a circular orbit 200 km above Earth s surface What is the minimum change in velocity Av that can be applied as an impulse to completely escape from Earth orbit In what direction should this impulse be applied relative to the orbital velocity at that instant Sketch the trajectory of such an escape showing Earth and the satellite What is the curve of that trajectory called Write the equation of that orbit in suitable coordinates and de ne the values of any coefficients g98 msz REanh6400km Solution The minimum escape speed is obtained simply by requiring conservation of energy U1 1 imv2 UfTf 0 R 2 0 V ZGM GM 2 R0 g R Z vRE 2 g64106ml jwllkms R0 6610 m The velocity of the satellite in orbit is obtained by requiring orbit equilibrium mv GMm GM g v R o R R0 E Era The minimum Av is obtained when the impulse is delivered parallel to the orbital velocity in that case 1 Av v V0 1 15 32kms The bounding trajectory between the family of ellipses orbits and hyperboli open trajectories is a parabola y R0 kx2 Now we must nd the appropriate value of k We require that the acceleration at perigee x0 in the above yx must be that produced by gravity y 2kx2 xj 2er G Af R0 GM 1 xv2 k 2 2 2ROV 4R0
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