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Instead of aiming to get into synchronous orbit, suppose the desire is to leave the earth entirely, on the way to some other planet. (i) If it were possible to launch straight east at the surface of the earth, what velocity (speed) would the spacecraft have to have to just barely be able to leave the earth behind, i.e. to go onto a parabolic trajectory. All elliptical trajectories to not escape from the earth, and hyperbolic trajectories have more energy than needed to escape. Use the earth mean radius, and of course ignore atmosphere, etc. (ii) If instead one starts in the 200 km altitude orbit, what speed would the satellite have to have to escape the earth?

Instead of aiming to get into synchronous orbit, suppose the desire is to leave the earth entirely, on the way to some other planet. (i) If it were possible to launch straight east at the surface of the earth, what velocity (speed) would the spacecraft have to have to just barely be able to leave the earth behind, i.e. to go onto a parabolic trajectory. All elliptical trajectories to not escape from the earth, and hyperbolic trajectories have more energy than needed to escape. Use the earth mean radius, and of course ignore atmosphere, etc. (ii) If instead one starts in the 200 km altitude orbit, what speed would the satellite have to have to escape the earth?

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Advanced Physics Instead of aiming to get into synchronous orbit, suppose the desire is to leave the earth entirely, on the way to some other planet. (i) If it were possible to launch straight east at the surface of the earth, what velocity (speed) would the spacecraft have to have to just barely be able to leave the earth behind, i.e. to go onto a parabolic trajectory. All elliptical trajectories to not escape from the earth, and hyperbolic trajectories have more energy than needed to escape. Use the earth mean radius, and of course ignore atmosphere, etc. (ii) If instead one starts in the 200 km altitude orbit, what speed would the satellite have to have to escape the earth?
Transcribed Image Text:Advanced Physics Instead of aiming to get into synchronous orbit, suppose the desire is to leave the earth entirely, on the way to some other planet. (i) If it were possible to launch straight east at the surface of the earth, what velocity (speed) would the spacecraft have to have to just barely be able to leave the earth behind, i.e. to go onto a parabolic trajectory. All elliptical trajectories to not escape from the earth, and hyperbolic trajectories have more energy than needed to escape. Use the earth mean radius, and of course ignore atmosphere, etc. (ii) If instead one starts in the 200 km altitude orbit, what speed would the satellite have to have to escape the earth?
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