Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has orbital speed v = 270 km/s, orbital period T= 15.0 days, and approximate mass m1 = 5.7M, where M, is the Sun's mass, 1.99 x 1030 kg. Assume that the visible star and its companion star, which is dark and unseen, are both in circular orbits (see the figure). Find the ratio of the approximate mass m2 of the dark star to Mg.

The Small Magellanic Cloud is a dwarf galay orbiting the Milky Way at a distance of 50 kiloparsecs from its center, on a circular orbit. It is moving at a velocity. rolative to the Milky Way, of 207 km/s. What is the mass of the Milky Way, in units of solar masses, inside the Cloud's orbit? B !! 245 If'a quasar emits 10^(10) times the Sun's luminosity, converting 10% of the mass of the material it eats into radiation, how many stars (ach of the Sun's mans) must it consume per year?

The Schwarzschild radius RBH for an object of mass M is defined as (See image.) where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M. In other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole.   1. The mass of the Sun is about 1.99 × 1030 kg. What would be the radius of a black hole with this mass?   2. The mass of Mars is about 6.42 × 1023 kg. What would be the radius of a black hole with this mass?   3. Suppose you want to make a black hole that is roughly the size of an atom (take RBH = 1.10 x 10-10 m). What would be the mass M of such a black hole?

Suppose you observe a binary system containing a main-sequence star and a brown dwarf. The orbital period of the system is 1 year, and the average separation of the system is 1 AU . You then measure the Doppler shifts of the spectral lines from the main-sequence star and the brown dwarf, finding that the orbital speed of the brown dwarf in the system is 23 times greater than that of the main-sequence star.  How massive is the brown dwarf in kg?

The radius Rh of a black hole is the radius of a mathematicalsphere, called the event horizon, that is centered on the blackhole. Information from events inside the event horizon cannotreach the outside world. According to Einstein’s general theory ofrelativity, Rh = 2GM/c2, where M is the mass of the black hole andc is the speed of light.Suppose that you wish to study a black hole near it, at a radialdistance of 50Rh. However, you do not want the difference in gravitationalacceleration between your feet and your head to exceed10 m/s2 when you are feet down (or head down) toward the blackhole. (a) As a multiple of our Sun’s mass MS, approximately what isthe limit to the mass of the black hole you can tolerate at the givenradial distance? (You need to estimate your height.) (b) Is the limitan upper limit (you can tolerate smaller masses) or a lower limit(you can tolerate larger masses)?

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 2

Two stars in a binary system, are seen edge-on from Earth. The HB line emitted by Star 1 varies between 486.162 nm and 486.186 nm, while that emitted by Star 2 varies between 486.140 nm and 486.208 nm. Assuming the stars are on a circular orbit, calculate the orbital velocity of the two stars and their mass ratio. What additional observational data is required to determine the mass of the system?

The velocity curve for a double 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. line 400 So = U, Ani 300 200 loo = v Ain i 100 -100 -200 -300 400 • 1 2 3 • s 7 a 10 Time (days) Find the mass of star 1, mı, in terms of solar masses. 1 solar mass = 2x1030kg Round your answer to three significant figures. Doppler Velocity (20su)

What 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

(Astronomy) PSR1913+16 Problem III. As the shape of the graph shown is not skewed, the orbit can be assumed circular. Also assume the system is viewed edge-on (that is, the orbital system is not inclined to the observer). Using these assumptions, the maximum radial velocities, and the orbital period T = 7.75 hours, find the orbital radii of the stars from the center of mass. (Hints: The figures below may be helpful. Use v = 2πr/P, where v is velocity, P is period, and r is radius. Note: redshifts have positive radial velocities values in the upper figure, whereas blueshifts have negative radial velocity values.)