13.5 Kepler's Laws of Planetary Motion

Conic sections as orbital paths, equal areas swept as a statement of angular momentum conservation, and period from the semi-major axis.

University Physics Volume 1, 13.5 Kepler's Laws of Planetary Motion

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5 exercises

13.5 Exercise 1

The nearly circular orbit of Saturn has an average radius of about 9.5 AU and has a period of 30 years, whereas Uranus averages about 19 AU and has a period of 84 years. Is this consistent with our results for Halley’s comet?

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13.5 Exercise 4

Calculate the mass of the Sun based on data for average Earth’s orbit and compare the value obtained with the Sun’s commonly listed value of $1.989 \times 10^{30} \text{kg}$ .

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13.5 Exercise 6

The “mean” orbital radius listed for astronomical objects orbiting the Sun is typically not an integrated average but is calculated such that it gives the correct period when applied to the equation for circular orbits. Given that, what is the mean orbital radius in terms of aphelion and perihelion?

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13.5 Exercise 8

The perihelion of the comet Lagerkvist is 2.61 AU and it has a period of 7.36 years. Show that the aphelion for this comet is 4.95 AU.

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13.5 Exercise 10

Eros has an elliptical orbit about the Sun, with a perihelion distance of 1.13 AU and aphelion distance of 1.78 AU. What is the period of its orbit?

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