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- Astronomers discover a binary system with a period of 90 days. Both stars have a mass twice that of the Sun. How far apart are the two stars? Both stars revolve around the center of mass in an orbit with radius r. F2oni d=ar Fron2 The distance between the stars is 2r.= 2000 K and a radius of R, A young recently formed planet has a surface temperature T Jupiter radii (where Jupiter's radius is 7 x 107 m). Calculate the luminosity of the planet and 2 determine the ratio of the planet's luminosity to that of the Sun.The mass of a star is 1.99·1031 kg and its angular velocity is 1.60E-7 rad/s. Find its new angular velocity if the diameter suddenly shrinks to 0.27 times its present size. Assume a uniform mass distribution before and after. Icm for a solid sphere of uniform density is 2/5 mr2.
- 2GM What is the escape velocity (in km/s) from the surface of a 1.6 Mo neutron star? From a 3.0 M. neutron star? (Hint: Use the formula for escape velocity, V. ; make sure to express quantities in units of meters, kilograms, and seconds. Assume a neutron star has a radius of 11 km and assume the mass of the Sun is 1.99 x 1030 kg.) 1.6 Mo neutron star km/s 3.0 Me neutron star km/sModels of the first star-forming clouds indicate that they had a temperature of roughly 150 K and a particle density of roughly 400,000 particles per cubic centimeter at the time they started trapping their internal thermal energy. ▼ Part A Estimate the mass at which thermal pressure balances gravity for these values of pressure and temperature. Express your answer in kilograms. —| ΑΣΦ Mcloud Submit Part B = Mcloud How does that mass compare with the Sun's mass? Express your answer in solar masses. Submit Request Answer = ΤΙ ΑΣΦ Request Answer ? ? kg MSun ReviewWhat is the Schwarzschild radius (in km) of a 6Msun black hole? What fraction of the Earth's radius is this? What percent of the speed of light (2.998 x 108 m/s) is the escape velocity at the Schwarzschild radius? Part 1 of 3 The Schwarzschild radius of a black hole is given by: 2GM Rs = c2 so for the given mass, 2G(6)(Msun) Rs c2 where M. Sun = 1.99 x 1030 kg. Then convert this into kilometers using 1 km = 1,000 m. Rs km
- The radius of a typical white dwarf star is a just a little larger than the radius of Earth, but a typical white dwarf has a mass that is similar to the Sun’s mass. Calculate the surface gravitational field strength of a white dwarf with a radius of 7 x 10^6 m and a mass of 1.2 x 10^30 kg. Compare this to the surface gravitational field strength of Earth.Small differences in the wavelengths in the sun’s spectrum are detected when measurements are taken from different parts of the sun’s disk. Specifi cally, measurements of the 656-nm line in hydrogen taken from opposite sides on the sun’s equator—one side approaching Earth and the other receding—differ from each other by 0.0090 nm. Use this information to fi nd the rotational period of the sun’s equator. Express your answer in days. (The sun’s equatorial radius is 6.96 x 108 m.)velocity curve for a double line spectroscopic binary is shown in the sketch. The system is viewed edge-on, i.e., with an inclination angle of i 90°, so that the maximum possible Doppler shifts for this system are observed. 400 SPo = , Ain i 300 200 l0o = v Ain i 100 -100 -200 -300 400 0 1 2 3 4 10 Time (days) Find the speed of star 2 in km/s. Doppler Velocity (2esu)
- While working with part of a research team you discover a set of exoplanets in a nearby star system. One of the planets is much closer to its mother star than the other and because of this you are able to determine the average radius of the closer planets orbit to be 37.26 x 10 to the 6 kilometers the Planet complete one orbit every 53.4 days. a) what is the mass of the star in this system?In a binary star system, two stars orbit about their common centre of mass, as shown in figure. If 12 = 2r1, what is the ratio of the masses m2/m, of the two stars? CM m2 2GMm F, r2 F(r = R) The surface gravity g of a body is. The acceleration due to gravity that an object m would feel on the surface of the body. A. Show that the surface gravity of Earth is ge = 9.8 m/s². B. Determine the surface gravity of the Sun. C. Determine the surface gravity of the Sun when it becomes a red giant star, assuming RG 1 AU. Use this answer to explain the significant mass loss rates observed in these objects.