Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 20, Problem 31Q
To determine
The mass of a white dwarf which has a diameter of
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Determining the orbit of the two stars of Kepler-34, also called A and B. These two stars together are called a binary.
A) Assume that star A has a mass of 1 solar mass and star B also has a mass of 1 solar mass. The semi major axis is 0.23 AU and the eccentricty is 0.53. What is the orbital period of the stellar A-B binary in days? Ignore the (much less massive) planet and focus on the orbit of the binary.
B) Now let's consider the orbit of the planet, called "b". Since the planet orbits some distance away from the stars, it is an acceptable approximation to pretend like the stellar binary is like a single star with a mass that is the sum of the masses of stars A and B and that the mass of planet "b" is very small, calculate the semi-major axis in AU of the planet's orbit with a period of 289 days.
(note: I think for this problem you are supposed to use Newton's version of Kepler's third law P2= 4π2/G(M1-M2)x a3 but, I'm not sure if that's the right thing to do).
1 solar mass= 2 x…
H5.
A star with mass 1.05 M has a luminosity of 4.49 × 1026 W and effective temperature of 5700 K. It dims to 4.42 × 1026 W every 1.39 Earth days due to a transiting exoplanet. The duration of the transit reveals that the exoplanet orbits at a distance of 0.0617 AU. Based on this information, calculate the radius of the planet (expressed in Jupiter radii) and the minimum inclination of its orbit to our line of sight.
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Analysis of the spectrum of a solar–mass star shows a periodic back-and-forth shift of its spectral lines with a period of 3 days. A spectral line centred at wavelength λ0 = 500 nm shows a shift ∆λ = ±2.5 × 10−4 nm. Estimate the mass of the unseen orbiting companion by assuming the angle of inclination i = 90◦, and express your answer in Jupiter masses.
Chapter 20 Solutions
Universe: Stars And Galaxies
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