imported>Patrick: Created page with 'The shuttle is in an orbit of radius $r$ which 5% smaller than rg. Therefore the radius of this orbit $r = 0.95 r_g$ . First we have to determine the radius…'

2011-09-30T03:49:17Z

Created page with 'The shuttle is in an orbit of radius <math>r</math> which 5% smaller than rg. Therefore the radius of this orbit <math>r = 0.95 r_g</math>. First we have to determine the radius…'

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The shuttle is in an orbit of radius <math>r</math> which 5% smaller than rg. Therefore the radius of this orbit <math>r = 0.95 r_g</math>.

First we have to determine the radius in the geosynchroneous orbit using Kepler's Law:

<math>r = \left ( {G M_E T^2 \over 4 \pi^2} \right )^{\frac{1}{3}} = \left ( {(6.67 \times 10^{-11})(6 \times 10^{24})(8.64 \times 10^4)^2 \over 4 \pi^2} \right )^{\frac{1}{3}} = 4.16 \times 10^7 m</math>
 
Then <math>r = 0.95 r_g = 0.95 \times 4.16 \times 10^7 = 3.94 \times 10^7 m</math> and the energy of the shuttle in this orbit is

<math>E_i = -\frac{1}{2}{G M_E m \over r} = -\frac{1}{2}{(6.67 \times 10^{-11})(6 \times 10^{24})(10^4) \over 3.94 \times 10^7} = -5.1 \times 10^{10} J</math>
 
To get into the geosynchroneous orbit the shuttle needs to have the energy

<math>E_f = -\frac{1}{2}{G M_E m \over r} = -\frac{1}{2}{(6.67 \times 10^{-11})(6 \times 10^{24})(10^4) \over 4.16 \times 10^7} = -4.8 \times 10^{10} J</math>
 
The boosters must provide the difference between these two energies.

<math>\Delta E = E_f - E_i = -4.8 \times 10^{10} - (-5.1 \times 10^{10}) = 3 \times 10^9 J</math>

Satellites and Binding Energy EX 13 - Revision history

imported>Patrick: Created page with 'The shuttle is in an orbit of radius r which 5% smaller than rg. Therefore the radius of this orbit r = 0.95 r_g. First we have to determine the radius…'

imported>Patrick: Created page with 'The shuttle is in an orbit of radius $r$ which 5% smaller than rg. Therefore the radius of this orbit $r = 0.95 r_g$ . First we have to determine the radius…'