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Planetary motion. A planet or asteroid orbits the Sun in an elliptical path'. The diagram shows two points of interest: point P, the perihelion, where the planet is nearest to the Sun, and the far point, or aphelion, at point A. At these two points (and only these two points), the velocity v of the planet is perpendicular to the corresponding "radius" vector 7, from the Sun to the planet. An arbitrary point Q is also shown.

Planetary motion. A planet or asteroid orbits the Sun in an elliptical path'. The diagram shows two points of interest: point P, the perihelion, where the planet is nearest to the Sun, and the far point, or aphelion, at point A. At these two points (and only these two points), the velocity v of the planet is perpendicular to the corresponding "radius" vector 7, from the Sun to the planet. An arbitrary point Q is also shown.

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Planetary motion. A planet or asteroid orbits the Sun in an elliptical path'. The diagram shows two points of interest: point P, the perihelion, where the planet is nearest to the Sun, and the far point, or aphelion, at point A. At these two points (and only these two points), the velocity v of the planet is perpendicular to the corresponding "radius" vector ř, from the Sun to the planet. An arbitrary point Q is also shown. P A
Transcribed Image Text:Planetary motion. A planet or asteroid orbits the Sun in an elliptical path'. The diagram shows two points of interest: point P, the perihelion, where the planet is nearest to the Sun, and the far point, or aphelion, at point A. At these two points (and only these two points), the velocity v of the planet is perpendicular to the corresponding "radius" vector ř, from the Sun to the planet. An arbitrary point Q is also shown. P A
Assume that the Sun is orders of magnitude more massive than the asteroid. This means the Sun does not accelerate significantly in response to the planet's gravity, and can be assumed to remain at rest. Derive a symbolic formula, but don't try too hard to simplify it. Look up the values and conversion factors you need in order to obtain a numerical answer. Recall the universal gravity formulas: —тMG Force p2 —тMG Potential energy Ug Consider the Sun-asteroid system to be isolated and apply conservation of energy. Also think about the system of the asteroid by itself. What influences are acting on the asteroid, and how do these affect its energy, momentum, and/or angular momentum? How can you write the asteroid's angular momentum (with respect to the Sun) at points A and P?
Transcribed Image Text:Assume that the Sun is orders of magnitude more massive than the asteroid. This means the Sun does not accelerate significantly in response to the planet's gravity, and can be assumed to remain at rest. Derive a symbolic formula, but don't try too hard to simplify it. Look up the values and conversion factors you need in order to obtain a numerical answer. Recall the universal gravity formulas: —тMG Force p2 —тMG Potential energy Ug Consider the Sun-asteroid system to be isolated and apply conservation of energy. Also think about the system of the asteroid by itself. What influences are acting on the asteroid, and how do these affect its energy, momentum, and/or angular momentum? How can you write the asteroid's angular momentum (with respect to the Sun) at points A and P?
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The law of conservation of angular momentum states that when no external torque acts on an object, no change of angular momentum will occur.  The law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be conserved over time

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