Mastering Physics Set 1 Midterm #1 Already Passed

A {Ans: Consider the earth following its nearly circular orbit (dashed curve) about the sun.(Figure 2) The earth has mass mearth=5.98×10^24kg and the sun has mass msun=1.99×10^30kg. They are separated, center to center, by r=93 million miles=150 million km. At the moment shown in the figure of the earth and sun (Figure 2) , what is the direction of the gravitational force acting on the earth? The possible directions are displayed in this figure (Figure 3) .}Find the escape velocity ve for an object of mass m that is initially at a distance R from the center of a planet of mass M. Assume that R≥Rplanet, the radius of the planet, and ignore air resistance. Express the escape velocity in terms of R, M, m, and G, the universal gravitational constant. {Ans: ve = sqrt(2GM/R)}Very far from earth (at R=∞), a spacecraft has run out of fuel and its kinetic energy is zero. If only the gravitational force of the earth were to act on it (i.e., neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash into the earth. The mass of the earth is Me and its radius is Re.