The gravitational force exerted by the planet Earth on a unit mass at a distancer from the center of the planet is GMr if rR where M is the mass of Earth, Ris its radius, and G is the gravitational constant. Is F a continuous function of r?

(a) Calculate the magnitude of the gravitational force exerted by Mars on a 65 kg human standing on the surface of Mars. (The mass of Mars is 6.4x1023 kg and its radius is 3.4x106 m.) 240.0277 ✓ N (b) Calculate the magnitude of the gravitational force exerted by the human on Mars. 240.0277 N (c) For comparison, calculate the approximate magnitude of the gravitational force of this human on a similar human who is standing 2.5 meters away. 1.76e8 XN (d) What approximations or simplifying assumptions must you make in these calculations? (Note: Some of these choices are false because they are wrong physics!) ✔Treat Mars as though it were spherically symmetric. Ignore the effects of the Sun, which alters the gravitational force that one object exerts on another. ✔Treat the humans as though they were points or uniform-density spheres. O Use the same gravitational constant in (a) and (b) despite its dependence on the size of the masses. Additional Materials eBook

Compute the gravitational attraction on a unit mass at the origin due to the mass (of constant density) occupying the volume inside the sphere r = 2a and above the plane z = a. Hint: The magnitude of the gravitational force on the unit mass due to the element of mass dM at (r, θ, φ) is (G/r2)dM. You want the z component of this since the other components of the total force are zero by symmetry. Use spherical coordinates.