A certain quaternary star system consists of three stars, each of mass m, moving in the same circular orbit of radius r about a central star of mass M. The stars orbit in the same sense and are positioned one-third of a revolution apart from one another. Show that the period of each of the three stars is given by
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Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
- Two stars of masses M and m, separated by a distance d, revolve in circular orbits about their center of mass (Fig. P11.50). Show that each star has a period given by T2=42d3G(M+m) Proceed as follows: Apply Newtons second law to each star. Note that the center-of-mass condition requires that Mr2 = mr1, where r1 + r2 = d.arrow_forwardCalculate the effective gravitational field vector g at Earths surface at the poles and the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force. How well does the result agree with the difference calculated with the result g = 9.780356[1 + 0.0052885 sin 2 0.0000059 sin2(2)]m/s2 where is the latitude?arrow_forwardSuppose the gravitational acceleration at the surface of a certain moon A of Jupiter is 2 m/s2. Moon B has twice the mass and twice the radius of moon A. What is the gravitational acceleration at its surface? Neglect the gravitational acceleration due to Jupiter, (a) 8 m/s2 (b) 4 m/s2 (c) 2 m/s2 (d) 1 m/s2 (e) 0.5 m/s2arrow_forward
- Let gM represent the difference in the gravitational fields produced by the Moon at the points on the Earths surface nearest to and farthest from the Moon. Find the fraction gM/g, where g is the Earths gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)arrow_forwardShow that for eccentricity equal to one in Equation 13.10 for conic sections, the path is a parabola. Do this by substituting Cartersian coordinates, x and y, for the polar coordinates, r and , and showing that it has the general form for a parabola, x=ay2+by+c .arrow_forwardTwo 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?arrow_forward
- Two stars M1 and M2 of equal mass make up a binary star system. They move in a circular orbit that has its center at the midpoint of the line that separates them. If M1 = M2 = 6.95 sm (solar mass), and the orbital period of each star is 2.45 days, find their orbital speed. (The mass of the sun is 1.99 1030 kg.)arrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 x 104 light-years from its center. (a) What should the orbital period (in y) of that star be? y (b) If its period is 5.3 x 107 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 massesarrow_forwardStars and black holes in a binary system orbit each other in circular orbits of radius r1 and r2 around their center of mass. Its mass is equal to 1.98x1030 kg, and its speed is 5.36 times faster than our Sun's. Furthermore, the visible star has an orbital period of 30 hours.(a) What is the apparent star's orbital radius, r1, in units of radii?In terms of MS, determine the black hole's mass m2. In the equation x3 = x(5a+5a)2, where an is the constant, x = 28a is a root.arrow_forward
- Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center. (a) What should the orbital period (in y) of that star be? y (b) If its period is 6.9 ✕ 107 y instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar massesarrow_forwardPlaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is V = 170 km/s and the orbital period of each is 13.7 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) solar masses M XCM Need Help? Read It Master Itarrow_forwardA certain triple-star system consists of two stars, each of mass m, revolving in the same circular orbit of radius r around a central star of mass M .The two orbiting stars are always at opposite ends of a diameter of the orbit. Derive an expression for the period of revolution of the stars.arrow_forward
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