You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 107 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 3 × 1011 m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 44.6 m/s2. What are the mass of (a) the planet and (b) the star? (G = 6.67 × 10-11 N · m2/kg2)

Irrigation channels that require regular flow monitoring are often equipped with electromagnetic flowmeters in which the magnetic field is produced by horizontal coils embedded in the bottom of the channel. a particular coil has 100 turns and a diameter of 6.0 m. when it's time for a measurement, a 4.5 a current is turned on. the large diameter of the coil means that the field in the water flowing directly above the center of the coil is approximately equal to the field in the center of the coil. the field is directed downward and the water is flowing east. the water is flowing above the center of the coil at 1.5 m/s . what is the magnitude of the field at the center of the coil? what is the direction of the force on a positive ion in the water above the center of the coil? what is the magnitude of the force on an ion with a charge +e?