 You have a mission. |
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| 1. You, the shuttle commander, are in a low Earth orbit. 375 km above sea level. You are to fire a 200 kg gps satelite module into a typical gps orbit (20,200 km). | |
| 2. You are to fuel the gps launcher engines with
fuel to give the gps module a kinetic energy boost that
will take the module to the new orbit, 22,200 km above
the Earth's surface. The module will be fired tangentially to the present orbit. |
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| 3. How much fuel do you need for the required energy boost? | |
| HINTS If you need more extensive hints, open the or |
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| 1. Draw the initial and final orbits. Draw the orbit that the gps module has to follow if it is to leave the low orbit tangentally and reach the high orbit tangentially. |
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| 2. Write down the expression for the angular
momentum of the module immediately after the energy boost
and as it reaches the high orbit. How is the velocity immediately after the energy boost related to the velocity of the module as it reaches the higher orbit. |
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| 3. How is the kinetic energy of the module as it reaches the higher orbit related to the kinetic energy of the module immediately after the boost and to the work that needs to be done against the gravity pull? | |
| 4. Calculate the kinetic energy that the module needs immediately after the boost if it is to complete the transfer as indicated. | |
| 5. Subtract the kinetic energy before the boost from the kinetic energy after the boost. | |
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| Ready for more? | Check out the
NASA Discussion of orbit transfer. If you do not have internet access, you can open a local version of the NASA document |