If Star B is discovered orbiting the same black hole once every 12years, find the orbital distance of Star B.
(Star A orbits the black hole at a distance of 2.5X10^14 m onceevery 24 yeares,mass of the black hole unknown)

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Sixta KovacekLv2

17 Dec 2019

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Theoretical question here on relativity and lengthcontraction:

If a neutron star of upper-limit mass is moving at a highlyrelativistic speed when viewed by an observer, then we know thatthe neutron star will appear to contract in the direction ofmotion.

Is it possible for the neutron star to appear to contractsufficiently enough so that its density becomes large enough to beconsidered a black hole (satisfies Schwarzschild radius) relativeto a stationary observer?

That is to say, is it possible for a stellar object to be a neutronstar in its rest frame but a black hole in the another frame ofreference? If so, what implications could that hold, would light beunable to escape it from the observer's frame (but possible toescape it from its rest frame)?

Black holes are objects whose gravitational field is so strong thatnot even light can escape. One way of thinking about this is toconsider a spherical object whose density is so large that theescape speed at its surface is greater than the speed of light, c.If a star's radius is smaller than a value called the Schwarzschildradius Rs, then the star will be a black hole, that is, lightoriginating from its surface cannot escape.
(a) For a nonrotating black hole, the Schwarzschild radius dependsonly upon the mass of the black hole. Show that it is related tothat mass M by Rs = (2GM)/c2.
(b) Calculate the value of the Schwarzschild radius for a blackhole whose mass is ten solar masses.
-----(ANSWER in km)

P.S. The problem gives the hint "Use conservation of energy, and anescape speed equal to the speed of light to derive the expressionfor the Schwarzchild radius of a non-rotating black hole."

Thank you so much for any help!

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. It has strayed too dose to a black hole having a mass 100 times that of the Sun (Fig. P13.7). The nose of the spacecraft points toward the black hole and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.)