imported>Patrick: Created page with 'Since the radius of the orbit is $r = 1.5 R_E$ , we have to use the general formula for the change in gravitational potential energy of the system satellite-Earth. The …'

2011-08-14T17:17:41Z

Created page with 'Since the radius of the orbit is <math>r = 1.5 R_E</math>, we have to use the general formula for the change in gravitational potential energy of the system satellite-Earth. The …'

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Since the radius of the orbit is <math>r = 1.5 R_E</math>, we have to use the general formula for the change in gravitational potential energy of the system satellite-Earth. The initial radius is <math>r_i = 1.5 R_E</math>. The final radius is 10% smaller, therefore <math>r_f = 0.9(1.5 R_E)</math>.

<math>\Delta U = {-G m_1 m_2 \over r_f} - \left ({-G m_1 m_2 \over r_i}\right ) = G m_1 m_2 \left (\frac{1}{r_i} - \frac{1}{r_f}\right )</math>
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Since <math>m_1 = M_E</math> and <math>m_2 = m_S</math>, we substitute for <math>r_i</math> and <math>r_f</math> and write

<math>\Delta U = G M_E m_S \left (\frac{1}{1.5 R_E} - \frac{1}{0.9(1.5 R_E)}\right ) = {G M_E m_S \over 1.5 R_E} \left (\frac{1}{1} - \frac{1}{0.9}\right ) = {-0.1 G M_E m_S \over 0.9(1.5 R_E)}</math>
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Substituting the values, we compute

<math>\Delta U = {-0.1(6.67 \times 10^{-11})(6 \times 10^{24})(500) \over 0.9(1.5(6.37 \times 10^6))} = -2.327 \times 10^9 J</math>

Potential Energy EX 5 - Revision history

imported>Patrick: Created page with 'Since the radius of the orbit is r = 1.5 R_E, we have to use the general formula for the change in gravitational potential energy of the system satellite-Earth. The …'

imported>Patrick: Created page with 'Since the radius of the orbit is $r = 1.5 R_E$ , we have to use the general formula for the change in gravitational potential energy of the system satellite-Earth. The …'