b Part b refers to the figure below In part a you should

Last updated: 6/3/2023

b Part b refers to the figure below In part a you should have found that the time it takes the Moon to go around the Earth is about 27 days For this problem we will take the orbital period of the Moon to be TM 27 days While the Moon is orbiting around the Earth the Earth is also spinning on its axis The rotational period for the Earth to spin on its axis is TE 1 day In the figure below at t 0 we first show a person on the Earth directly opposite the Moon At t 12 hrs day the Earth did a half rotation and the Moon moved along its orbit At t 24 hrs 1 day the Earth did a full rotation and the 24 hrs Moon moved along its orbit Notice the person is not directly opposite the Moon at t 1 day since the Moon moved on its orbit At the time t the person is directly opposite the Moon again What is the time t for the person to be opposite the Moon again Hints Notice that at the time t the angle is the same for the person on the Earth and the Moon Thus we can use the equation OE OM to find t In this equation 0g is the angle the Earth makes and M is the angle the Moon makes Since the Earth and the Moon are rotating at constant speeds 0 wt where w 27 T Lastly when writing the equation OE OM you need to take into account that the Earth has done one full rotation and then the Earth rotates an angle 0 The angle for one full rotation in radians is the angle of a circle 27 You should find t to be close to 24 hours and 50 minutes This calculation shows us that the high tide on a place on the Earth occurs 50 minutes later the next day t 0 t 12 hrs or 1 t ONE 2 day Part b t 24 hrs or t 1 day t