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

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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2. Two identical stars with radius R and mass M, orbits around their center of mass. The orbit is circular, and the stars are always on the opposite side of the circle. (b) Find the orbital speed of each star and their periods.
The moon on Mars Phobos ( Fear) and Deimos ( Terror) are very close to the planet compared to Earth's Moon. Their orbital radii are 9,376 km and 23,463.2 km respectively. A) what is the orbital speed of Phobos to that of Deimos? B) If the period of Phobos orbits 7hr 39.2 min, what is the mass of Mars? C) Calculate the orbital period of Deimos.
10) Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun). _____ m
Planet X with a radius of 4.0 Rearth⊕ is found orbiting a star of mass 0.80M⊙ . The eccentricity of its orbit is 0.05, and at its farthest approach to the star, it is 0.63 AU away, while at its closest approach to the star, it is 0.57 AU away. a. How long does it take Planet X to make a complete orbit around its star in years? b.The semi major axis of the planet is changed such that its closest approach to the star is now 2.9 AU. Would the gravitational force exerted by the star on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor? c. The mass of the star was increased to 2.4M⊙ . Would the gravitational force exerted by it on Planet X increase or decrease? By what factor? Would the gravitational force exerted by Planet X on the star increase or decrease? By what factor? d. What must the mass of Planet X be in Mearth⊕ such that an astronaut on its surface would have the same weight as…
2. The planet Jupiter has an orbital period of 4332.8 days, and its greatest distance (aphelion distance) from the Sun is 5.455 AU {where 1 AU = 1 Astronomical Unit = 1.496x10'' m}. The mass of the planet Jupiter is 1.898x1027 kg and the mass of the Sun is 1.988x1030 kg. {G = 6.67x10'" Nm/kg?) (a) Calculate the perihelion distance (closest distance) in Astronomical Units (AU) of the planet Jupiter from the Sun. (b) Calculate the eccentricity of planet Jupiter's orbit around the Sun. (c) Calculate the smallest speed of planet Jupiter around the Sun in km/s. At what point in Jupiter's orbit does Jupiter have its smallest speed?
010: A new planet (tentatively named "Melmac") is found in a circular orbit with a period of 571 years. The sun has a mass of 1.9891x1030 kg. How far away is the planet in Astronomical Units (AU) ? Note: An A.U. is 1.496x1011 m.
6.
6
2. Does the rotation of the Earth contribute to its mass? If so, how much? If not, why not? (Assume the Earth is spherical with uniform density.) You may need to know its radius is 6.38 x 103 km, mass is 5.98 x 1024 kg, and one day is 8.64 x 104 s.
11 Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 10- solar masses. A star orbiting near the galaxy's periphery is 5.9 x 10" light-years from its center. (a) What should the orbital period (in y) of that star be? y. (b) If its period is 6.1 x 10' years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of the Milky Way. solar masses
Part A Kepler's Third "Law" states that the square of the orbital period of a planet (T) is proportional to the cube of the planet's average orbital radius (r), T² = kr³, where k is the proportionality constant connecting T2 and We can derive Kepler's Third "Law" and show that k = 4/Gmgun, where G is the universal gravitational constant and msun is the mass of the sun, by %3D preventing a global thermonuclear war before it ruins our day and then binge watching the first ten seasons of the Walking Dead on Netflix. setting the acceleration due to gravity at the surface of the planet equal to the acceleration due to gravity at the surface of the sun. O setting the mutual gravitational force between the planet and the sun, Gmplanetmsunr, equal to the centripetal force acting on the planet. O stealing Robert Hooke's undeveloped idea that the mutual attractive force between the planet and the sun is proportional to 1/2. convincing ourselves that planets in circular orbits are actually in…

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