Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Chapter 2, Problem 2.49P
To determine
Show that the period is proportional to
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Two stars M, and M, 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
M, - M, - 1.45 sm (solar mass), and the orbital period of each star is 1.70 days, find their orbital speed. (The mass of the sun is 1.99 x 10 kg.)
km/s
M,
A 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.
Plaskett'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| = 225 km/s and the orbital period of each is 11.6 days. Find the mass M
of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.)
M
XCM
M
Part 1 of 3 - Conceptualize
From the given data, it is difficult to estimate a reasonable answer to this problem without working through
the details and actually solving it. A reasonable guess might be that each star has a mass equal to or slightly
larger than our Sun because fourteen days is short compared to the periods of all the Sun's planets.
Part 2 of 3 - Categorize
The only force acting on each star is the central gravitational force of attraction which results in a centripetal
acceleration. When we solve Newton's second law, we can find the unknown mass in terms of the variables…
Chapter 2 Solutions
Classical Dynamics of Particles and Systems
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - If a projectile is fired from the origin of the...Ch. 2 - A clown is juggling four balls simultaneously....Ch. 2 - A jet fighter pilot knows he is able to withstand...Ch. 2 -
In the blizzard of ’88, a rancher was forced to...Ch. 2 - Prob. 2.7PCh. 2 - A projectile is fired with a velocity 0 such that...Ch. 2 - Consider a projectile fired vertically in a...Ch. 2 - Prob. 2.11P
Ch. 2 - A particle is projected vertically upward in a...Ch. 2 -
A particle moves in a medium under the influence...Ch. 2 - A projectile is fired with initial speed 0 at an...Ch. 2 -
A particle of mass m slides down an inclined...Ch. 2 - A particle is projected with an initial velocity 0...Ch. 2 - A strong softball player smacks the ball at a...Ch. 2 - Prob. 2.19PCh. 2 - A gun fires a projectile of mass 10 kg of the type...Ch. 2 - Prob. 2.21PCh. 2 - Prob. 2.22PCh. 2 - A skier weighing 90 kg starts from rest down a...Ch. 2 - A block of mass m = 1.62 kg slides down a...Ch. 2 - A child slides a block of mass 2 kg along a slick...Ch. 2 - A rope having a total mass of 0.4 kg and total...Ch. 2 - A superball of mass M and a marble of mass m are...Ch. 2 - An automobile driver traveling down an 8% grade...Ch. 2 - A student drops a water-filled balloon from the...Ch. 2 - Prob. 2.31PCh. 2 - Two blocks of unequal mass are connected by a...Ch. 2 - A particle is released from rest (y = 0) and falls...Ch. 2 - Perform the numerical calculations of Example 2.7...Ch. 2 - Prob. 2.36PCh. 2 - A particle of mass m has speed υ = α/x, where x is...Ch. 2 - The speed of a particle of mass m varies with the...Ch. 2 - A boat with initial speed υ0 is launched on a...Ch. 2 - A train moves along the tracks at a constant speed...Ch. 2 - Prob. 2.42PCh. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - Consider a particle moving in the region x > 0...Ch. 2 - Prob. 2.48PCh. 2 - Prob. 2.49PCh. 2 - According to special relativity, a particle of...Ch. 2 - Let us make the (unrealistic) assumption that a...Ch. 2 - A particle of mass m moving in one dimension has...Ch. 2 - A potato of mass 0.5 kg moves under Earth’s...Ch. 2 - Prob. 2.55P
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- 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_forwardModel the Moons orbit around the Earth as an ellipse with the Earth at one focus. The Moons farthest distance (apogee) from the center of the Earth is rA = 4.05 108 m, and its closest distance (perigee) is rP = 3.63 108 m. a. Calculate the semimajor axis of the Moons orbit. b. How far is the Earth from the center of the Moons elliptical orbit? c. Use a scale such as 1 cm 108 m to sketch the EarthMoon system at apogee and at perigee and the Moons orbit. (The semiminor axis of the Moons orbit is roughly b = 3.84 108 m.)arrow_forwardTwo 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_forward
- Plaskett'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| = 200 km/s and the orbital period of each is 11.5 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 Marrow_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_forwardIn the time of Johannes Kepler, it was believed that the orbit of Earth was circular, whereas the orbit of Mars was believed to be an oval (perhaps an ellipse), whose minor axis is 0.5% shorter than its major axis, so (a − b)/a ≈ 0.005. It was also known that the Sun is not at the center of this orbit; it is offset by about 10% of a. Kepler knew the geometry of ellipses very well, and recognized that this information made it quite likely that the orbit of Mars was actually an ellipse. Explain how he might have reached this conclusion (which was confirmed theoretically by Isaac Newton a half-century later).arrow_forward
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