The orbital period of the Moon around Earth is 27.32 days; that of Earth around the Sun is 365.26 days.

(a) Which orbit has the greater rotational speed: Earth's or the Moon's? Are the orbital rotational speeds of Earth and the Moon around the Sun great or small relative to the rotational speeds you encounter in daily life?

(b) The radius of the Moon's orbit around Earth is \(R_{\mathrm{M}}=3.84 \times 10^{8} \mathrm{~m}\); that of Earth's orbit around the Sun is \(R_{\mathrm{E}}=1.50 \times 10^{11} \mathrm{~m}\). Which has the greater speed?

(c) Calculate the centripetal acceleration of Earth in the reference frame of the Sun and the centripetal acceleration of the Moon in the reference frame of Earth.

(d) How do these accelerations compare with the acceleration due to gravity near Earth's surface?