Answer to Question #91090 in Mechanics | Relativity for Rose

Question

A spaceship is shaped like a giant bicycle wheel. The wheel has a diameter of 1.2km. The spaceship can simulate gravity by spinning.
A. How fast does the wheel need to spin so that the artificial gravity felt by the station inhabitants is the same in earth?
B. The space station mass is 8.35 x 10^7 kg is orbiting plant x with Mass of 2.3 x 10^22 kg at the distance r=113.2 x 10^6m. What is the force of gravity between the planter and the space station?
C. The space station has a satellite that orbits Planet X at an orbital radius of 250 000km. How fast is the satellite moving?
D. In the same solar system a back hole mass: 1.3 x 10^32. The space station has a satellite that orbits the black hole at a radius of 151km. How fast is the satellite moving?

Answer 1

a.

$$\omega=\sqrt{\frac{g}{r}}=\sqrt{\frac{9.8}{600}}=0.13\frac{rad}{s}$$

b.

$$F=\frac{GmM}{R^2}=\frac{(6.67\cdot 10^{-11})(8.35\cdot 10^7)(2.3\cdot 10^{22})}{(113.2\cdot 10^6)^2}=10000\ N=10\ kN$$

c.

$$v=\sqrt{\frac{GM}{r_s}}=\sqrt{\frac{(6.67\cdot 10^{-11})(2.3\cdot 10^{22})}{(250\cdot 10^6)}}=78\frac{m}{s}$$

d.

$$v'=\sqrt{\frac{GM'}{r'_s}}=\sqrt{\frac{(6.67\cdot 10^{-11})(1.3\cdot 10^{32})}{(151\cdot 10^3)}}=2.4\cdot 10^8\frac{m}{s}$$