Astronomy Problems (Homework) 4 Solutions

Astronomy Problems (Homework) 4 Solutions - Homework 4...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 4 University Astronomy 5/10/10 1 University Astronomy 1017-301 Homework Assignment 4 Instructor: Dr Andrew Robinson Due Date: Friday, 4 May 2010. To tackle some of the following problems you will need to do some research, using either the textbook or other resources, to find various pieces astronomical data and the values of certain physical constants. For calculations, show all your workings in order to receive full credit . 1. Calculate the main sequence lifetimes of the following stars a. An O star that has a luminosity 6 × 10 4 L (solar luminosities). b. An F star that has a luminosity 3 L . c. An M star that has a luminosity 0.03 L . Use the fact that the Sun has an estimated main sequence lifetime of 12 billion years. 2. Following the arguments given in Lecture 15, estimate the length of time that each of the stars in problem 2 could shine by their gravitational energy alone. At what stage in a star’s life does it shine mainly by the release of gravitational energy? Hint: to do the calculation you will first need to calculate values for the radius of each star. The surface temperatures given in Lecture 11 or in Table 15.1 in the textbook will help here. From Lecture 15, the main sequence lifetime is t ~ E/L, where E = energy content and L = luminosity. Since the energy comes from nuclear fusion E Mc 2 , where M = mass of star, so t M/L. We can make use of the mass-luminosity relation, L M 3.5 , to eliminate M (or L), to get t L -5/7 . Scaling to the Sun, t = (L /L) 5/7 t , where t is the sun’s main- sequence lifetime. Therefore, a) O star t = (1/6x10 4 ) 5/7 x1.2x10 10 y 4.6x10 6 y b) F star t = (1/3) 5/7 x1.2x10 10 y 5.5x10 9 y c) M star t = (1/0.03) 5/7 x1.2x10 10 y 1.5x10 11 y From Lecture 15, t grav ~ 1/2|U|/L where |U|~3GM 2 /5R, and R is the radius of the star. We know L from the information given in question 1, and we can get M from the mass-luminosity relation, but we don’t know R. Continued…
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Homework 4 University Astronomy 5/10/10 2 3. We saw in Lecture 15 that there is a maximum mass for main sequence stars, which is set by the condition that the Eddington limit is not exceeded. Show that if main sequence stars follow a mass-luminosity relationship of the form L " M 3.5 , the maximum mass is 60 M . 4. Spectroscopic observations of an A star reveal that it is in an eclipsing binary system with an unseen companion. Measurements of the Doppler shifts of certain absorption lines in the star show cyclical variations with a period of 3.65 days. The extreme red- and blue-shifts are both equal to 300 km/s. Estimate the total mass of the system and
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern