A) Starbuck knows the Earth has a mass of 5.98 x 10" kg and its radius is 6380 km. The Sun has a mass of 1.99 x 1050 kg and a radius of 696000 km. The Earth orbits the Sun with an average orbital radius of on astronomical unit (1.49 * 10 m). Determine the force of gravity between the Earth and Sun. The force of gravity provides the centripetal force acting on the Earth while it revolves around the Sun. I) Determine the speed of the Earth in its orbit around the Sun in km/h and Mach (Mach 1 = 341 m/s & 10 m/s =36 km/h). II) Determine the period of the Earth's orbit around the Sun and then compare your answer to the accepted value of 365.26 days where a day is 86 400 s. B) Captain Kirk wishes to determine the speed of an electron inside a hydrogen atom using the Bohr-Rutherford model of the atom. He attempts to use Newtonion physics, foolishly ignoring special relativity and quantum mechanics. The masses of a proton and electron are 1.67 x 10 2kg and 9.11 x 103 kg respectively. They also have electrical charges of +le and -le respectively where is e the elementary charge is 1.6 x 10 19C. The average orbital radius of the electron in the first orbital shell is 5.3 x 10 " m. Using the Bohr-Rutherford model the centripetal force should be provided by the gravitational and electric forces between the proton and electron. I) Check to see if the gravitational force is negligible relative to the electric force. II) Calculate the average speed of the electron orbiting around the proton in the hydrogen atom and compare it to the speed of light c (ex v = 0.95 c). III) Determine the frequency of the electron orbiting the nucleus. C) Captain Sisko observes an electron circling in a smoke box at the surface of the Earth where the magnetic field is 45 uT [Up]. The electron's centripetal motion has a radius of 10 cm. Determine speed of the electron and covert the answer in to Mach or c (ex. Mach 10 where Mach 1 = 341 m/s, or 0.10 c where c is the speed of light). For now on convert all m/s answers into a more reasonable units of measurement