In a binary-star system, each star has teh same mass which is 4.1 times of that
ID: 1554160 • Letter: I
Question
In a binary-star system, each star has teh same mass which is 4.1 times of that of the Sun. I need help with this prblem please #57. # 65, #74. Please show your work so that i can follow how you got your answer.
Can you please show your work help with prolblems 57, 65 and 74. Thank you!
(a) Number Units (b) Number '2 Units significant digits are disabled; the tolerance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits are disabled; the tolerance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits are disabled the tolerance is +/-2% 10 significant digits are disabled; the tolerance is +/-2% significant digits are disabled; the tolerance is +/-2% Chapter 13, Problem 040 A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.714 of the escape speed from Earth and (b) its initial kinetic energy is 0.714 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth? (a) Number Units (b) Number Units (c) Number Units significant digits are disabled, the toierance is +/-2% significant digits are disabled, the tolerance is +/-2% significant digits not applicable, exact number, no tolerance Chapter 13, Problem 057 In a certain binary-star system, each star has the same mass which is 4.1 times of that of the Sun, and they revolve about their center of mass. The distance between them is the 1.7 times the distance between Earth and the Sun. What is their period of revolution in years?Explanation / Answer
chapter 13 problem 57
From gravitation F = GMM/R^2
and for the rotation the radius of rotation is R/2 as they are rotating about the midway point
so F = M w^2 R/2
w ^2 = 2 F / (MR) = 2 GMM / (MR^3) = 2GM/R^3
as w= 2pi()/T then
T^2/(2pi())^2 = r^3/ (2GM)
T^2 = (2 pi()) ^2 * R^3 /( 2GM)
T = 2pi() sqrt( R^3 / (2GM)
Note that compared to your formula there is a factor of 2 in the denominator that you do not have.
This is because we have a binary star system rotating about a common origin rather than a small body rotating about a central star.
With this you should be able to complete the problem successfully.