Because Earth rotates about its axis once every 24h, a launch from the equator receives an eastward “boost” due to Earth’s surface motion. Neglect atmospheric effects and treat Earth as an isolated sphere of mass 5.97×1024kg and radius 6.37×106m.
(a) Calculate the magnitude of Earth’s tangential surface speed at the equator due to rotation.
(b) Derive an algebraic expression for the *additional* launch speed (relative to the ground) that must be supplied to a spacecraft at the equator so that, after taking advantage of Earth’s rotational speed found in part (a), the spacecraft will still escape Earth’s gravitational influence.
(c) Evaluate the expression from part (b) numerically, then determine by what percentage this required launch speed is reduced compared with the escape launch speed needed from a hypothetical non-rotating Earth.
(d) Briefly discuss one practical implication of your result for the selection of launch sites on Earth.