Given that Newton's Law of gravity makes the gravitational potential energy negative, we have the very...

 

 

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Given that Newton's Law of gravity makes the gravitational potential energy negative, we have the very intriguing possibility that a satellite could have a total energy of zero! (a.) What special condition must the kinetic and gravitational potential energies obey in order for the total energy to be zero. (b.) Show that the angular-momentum conservation condition derived in class for the speed and distances at apogee and perigee (or aphelion and perihelion for something in orbit around the sun) vara Upp, makes it impossible for a satellite in elliptical orbit to have a total energy of zero but that it could happen in circular orbit. Hint: Write an equation for the energy at apogee and one for the energy at perigee. Show that if one of them equals zero, that the vara Upp condition requires that other one cannot be zero unless the orbit is circular. = (c.) In fact, explain why it makes sense that the total energy of a satellite would be negative. Hint: Use the same argument as the one used in class when deriving the escape speed equation. Given that Newton's Law of gravity makes the gravitational potential energy negative, we have the very intriguing possibility that a satellite could have a total energy of zero! (a.) What special condition must the kinetic and gravitational potential energies obey in order for the total energy to be zero. (b.) Show that the angular-momentum conservation condition derived in class for the speed and distances at apogee and perigee (or aphelion and perihelion for something in orbit around the sun) vara Upp, makes it impossible for a satellite in elliptical orbit to have a total energy of zero but that it could happen in circular orbit. Hint: Write an equation for the energy at apogee and one for the energy at perigee. Show that if one of them equals zero, that the vara Upp condition requires that other one cannot be zero unless the orbit is circular. = (c.) In fact, explain why it makes sense that the total energy of a satellite would be negative. Hint: Use the same argument as the one used in class when deriving the escape speed equation.

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