6. A certain binary star system consists of two identical stars of mass M,each moving in a circular orbit of radius R about a center of mass locatedhalfway the two stars as shown. Calculate the following:(a) the gravitational force exerted on each star(b)the orbital speed of each star(c)the period of the orbital motion of each star(d)the energy needed to separate the two stars to an infinitedistance from each other.MRCENTER-OFMASSM

Answered: Image /qna-images/answer/6b3c8f98-1a39-450e-9f54-1e58c58bec1c.jpg

Answered: 6. A certain binary star system…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter39: Relativity

Section: Chapter Questions

Problem 1PQ

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Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital Speed using the following information: The mass of the galaxy is equivalent to a single mass times that at the Sun (or located 30,000 ly away.
A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. a. One of these stars is believed to be in an approximately circular orbit with a radius of about 1.50 103 AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting, b. What is the speed of this star, and how does it compare with the speed of the Earth in its orbit? How does it compare with the speed of light?
Astronomical observatrions of our Milky Way galaxy indicate that it has a mass of about 8.01011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0104 light-years from its center. (a) What should the orbital period of that star be? (b) If its period is 6.0107 years instead, what is the mass 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.
Assuming a circular orbit for the Sun about the center of the Milky Way Galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass 1.51011times that of the Sun (or 31014kg ), located 30,000ly away.
Two double stars, one having mass 1.0 Msun and the other 3.0 Msun, rotate about their common center of mass. Their separation is 6 light years. What is their period of revolution?
In what frame(s) of reference are Kepler's laws valid? Are Kepler's laws purely descriptive, or do they contain causal information?
Using the solution from the previous problem, find the increase in rotational kinetic energy, given the core’s mass is 1.3 times that of out Sun. Where does this increase in kinetic energy come from?
What is the orbital radius of an Earth satellite having a period of 1.00 h? (b) What is unreasonable about this result?
For many years, astronomer Percival Lowell searched for a Planet X that might explain some of the perturbations observed in the orbit of Uranus. These perturbations were later explained when the masses of the outer planets and planetoids, particularly Neptune, became better measured (Voyager 2). At the time, however, Lowell had proposed the existence of a Planet X that orbited the Sun with a mean distance of 43 AU. With what period would this Planet X orbit the Sun?
Find the speed needed to escape from the solar system starting from the surface of Earth. Assume there are no other bodies involved and do not account for the fact that Earth is moving in its orbit. [Hint: Equation 13.6 does not apply. Use Equation 13.5 and include the potential energy of both Earth and the Sun. Substituting the values for Earth’s mass and radius directly into Equation 13.6, we obtain vesc=2GMR=2(6.67 10 11Nm2/kg2)(5.96 10 24kg)(6.37 106m)=1.12104m/s That is about 11 km/s or 25,000 mph. To escape the Sun, starting from Earth’s orbit, we use R=RES=1.501011m and MSum=1.991030kg . The result is vesc=4.21104m/s or about 42 km/s. We have 12mvesc2GMmR=12m02GMm=0 Solving for the escape velocity,
Two planets in circular orbits around a star have speed of v and 2v . (a) What is the ratio of the orbital radii of the planets? (b) What is the ratio of their periods?
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