The distance between the Earth and the Moon is about 384 400 km. a) Determine the mass of the earth. Gravitational constant G=6.67259E-11 Nm^2/kg^2. (3 points) (HINT: N II! Centripetal acceleration a-v^2/r, where v is the tangential speed and r is the radius of curvature of the orbit. Let's assume the moon's orbit around the earth to be a circle. It may help to 'estimate the length of the month.) b) Why doesn't the result quite match the generally accepted estimate of 5.974E24 kg? (1 point) What should e.g. the length of the month be in order to match? (1 point) c) Calculate the magnitude of the acceleration caused by the gravitational force F caused by the Earth's mass M on the body of mass m on the Earth's surface. The radius of the earth is about 6365 km. (1 point) HINT: gravitational force F of point masses m and M: F=GmM/r^2. The connection of the object's gravity F to the mass m is usually presented briefly in the form F=mg. d) How large an acceleration does the Earth cause to the Moon? (1 point)