Question

the milky way is held together by a black holes gravitational force. since the stars near this black hole move at a high speed, what can you infer about the black hole? a) its location b) its size c) its speed d) its depth

Explanation:

According to the law of universal gravitation, the gravitational force \(F = G\frac{Mm}{r^{2}}\), where \(M\) is the mass of the black - hole, \(m\) is the mass of the star, \(r\) is the distance between them, and \(G\) is the gravitational constant. The centripetal force \(F_{c}=m\frac{v^{2}}{r}\) for a star moving in a circular orbit around the black - hole. Equating \(F = F_{c}\), we get \(v=\sqrt{\frac{GM}{r}}\). When the speed \(v\) of the star is high, if \(r\) (the distance from the star to the black - hole) is relatively constant (for stars near the black - hole), a large \(v\) implies a large \(M\). A large mass black - hole will have a large size (in terms of the event - horizon radius \(R = \frac{2GM}{c^{2}}\), where \(c\) is the speed of light). The location of the black - hole is already known (as it's the center of the Milky Way's gravitational binding). The speed of the black - hole itself is not related to the star's speed in this context (the star's speed is due to the black - hole's gravitational pull). Depth is not a relevant property in this astrophysical gravitational - force - related inference.

Answer:

B) Its size