7. Kepler's Third Law relates the period (P) it takes a planet to go around the Sun in an orbit of a givensemi-major axis (a). Assume that the mass of the Sun is much, much greater than any of the planets(which it is), and measure P in years and a in astronomical units. The simplified relationship (formula)is:P =aThe following two orbits have the same value for a. How do their values of P compare?

On the basis of eccentricity, we can compare the period values. As can be seen in the diagram, the…

Answered: 7. Kepler's Third Law relates the…

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter2: Kinematics

Section: Chapter Questions

Problem 10PE: Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is...

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Similar questions

Use Keplers second law to convince yourself that Earth must move faster in its orbit during the northern hemisphere winter, when it is closest to the Sun, than during the summer, when it is farthest from the Sun.
Why did Greek astronomers conclude that the heavens were made up of perfect crystalline spheres moving at constant speeds?
Tidal friction is slowing the rotation of the Earth. As a result, the orbit of the Moon is increasing in radius at a rate of approximately 4 cm/year. Assuming this to be a constant rate, how many years will pass before the radius of the Moon's orbit increases by 3.84106 m (1%)?
What, on a sphere, is analogous to a two-dimensional Cartesian coordinate system?
What evidence can you cite that planets orbit other stars?
How did the Ptolemaic model explain retrograde motion?
If a planet had an average distance from the Sun of 10 AU, what would its orbital period be?
Review. In 1963, astronaut Gordon Cooper orbited the Earth 22 times. The press stated that for each orbit, he aged two-millionths of a second less than he would have had he remained on the Earth. (a) Assuming Cooper was 160 km above the Earth in a circular orbit, determine the difference in elapsed time between someone on the Earth and the orbiting astronaut for the 22 orbits. You may use the approximation 11x=1+x2 for small x. (b) Did the press report accurate information? Explain.
What is the gravitational acceleration close to the surface of a planet with a mass of 2ME and radius of 2RE where ME, and RE are the mass and radius of Earth, respectively? Answer as a multiple of g, the magnitude of the gravitational acceleration near Earths surface. (See Section 7.5.)
(a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter, (b) The largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 109 m and a period of 7.16 days. Calculate the mass of Jupiter from this data, (c) Are your results to parts (a) and (b) consistent? Explain.
The vernal equinox and the autumnal equinox are associated with two points 180 apart in the Earths orbit. That is, the Earth is on precisely opposite sides of the Sun when it passes through these two points. From the vernal equinox. 185.4 days elapse before the autumnal equinox. Only 179.8 days elapse from the autumnal equinox until the next vernal equinox. Why is the interval from the March (vernal) to the September (autumnal) equinox (which contains the summer solstice) longer than the interval from the September to the March equinox rather than being equal to that interval? Choose one of the following reasons, (a) They are really the same, but the Earth spins faster during the summer interval, so the days are shorter, (b) Over the summer interval, the Earth moves slower because it is farther from the Sun. (c) Over the March-to-September interval, the Earth moves slower because it is closer to the Sun. (d) The Earth has less kinetic energy when it is warmer, (e) The Earth has less orbital angular momentum when it is warmer.
An object of mass m is located on the surface of a spherical planet of mass M and radius R. The escape speed from the planet does not depend on which of the following? (a) M (b) m (c) the density of the planet (d) R (e) the acceleration due to gravity on that planet

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