12.4 (a) What is the average density of the sun? (b) What is the av- erage density of a neutron star that has the same mass as the sun but a radius of only 20.0 km?
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In Exercise 12.4 of your book, University Physics 15th edition (see End of the Chapter 12 section), what is the answer for sub-item (b) if the radius of the neutron star is 59.531 km? (express your answer in the proper SI unit and without scientific notation)
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- what is the answer for sub item (b) if the radius of the neutron star is 69.601 km? (express your answer in the proper SI unit ans without scientific notation)Suppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe? Values: m = 4 kg r = 0.0407 m Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3)a)Define the term “standard candle” as used in cosmology. b)The flux is defined asf(Dlum) = L/4πD^2lumwhere L is the absolute luminosity and Dlum is the distance to the radiation source (youmay assume z ≪ 1).Assume that we have measured the flux to be f = 7.234 10^−23 Wm^−2 and the absoluteluminosity is given by L = 3.828 x10^26W. Calculate the luminosity distance D lum to the objectin Mpc.
- In Exercise 12.4, what is the answer for sub-item (b) if the radius of the neutron star is 70.617 km? (express your answer in the proper SI unit and without scientific notation)Of 1.5, 3, 5, and 10 give the maximum apparent speeds. 2. Consider a relativistic jet with an angle of 70 degrees relative to the line of sight (i.e. it is almost, but not quite perpendicular to the line of sight). Let its value of gamma for the motion be 3. (a) Will it appear superluminal? (b) Will it appear to be brighter or fainter than it would in its own rest frame? 3. State whether the following reactions are possible under special relativity. If not, explainScientists are conducting an experiment to determine if their hypothesis that a certain constant in the universe is 1.65. the uncertainties in the experiment result in a relative uncertainty of no more than 2%. After several experimental trials, the scientists obtained an average value of 1.7 for the constant. What can be said about the scientists hypothesis? Hint calculate the percent error and compare it to the relative uncertainty.
- Compute the life expectancy of a 1.5M⊙ star.For a circular velocity profile of the type Θ(r)=αr3/10Θ(�)=��3/10, where α� is a constant and r� is the radial distance from the centre of a spiral galaxy, find the ratio κ(r)/Ω(r)�(�)/Ω(�), where κ(r)�(�) is the epicyclic frequency and Ω(r)Ω(�) is the angular velocity. Enter your answer to 2 decimal places.3. Let's imagine that the earth is shrinking and we want to escape before it is too late. Let's set up some notation: R: the radius of Earth MẸ : the mass of Earth m: your mass G : the universal gravitational constant c: the speed of light Note that, since Earth is shrinking, R is not constant, but MẸ is constant (the values of ME, G and c are available on Wikipedia). In this question, we will compute the velocity needed to escape Earth and the radius of (shrunken) Earth for which even light cannot escape (when Earth becomes a black hole). In fact, all of the related formulae are well known and the purpose of this question is to justify our work using what we have learned in this course so far. (a) The work (energy) W needed to free yourself from Earth when its radius is R metres is w = G ME m dh. h2 R Show that this improper integral is equal to GME m R