Climbing to the top of Mount Everest is hard, but it's slightly easier than you might think as people weigh less as they climb to the top. Let be a person's weight on top of Mount Everest and be their weight at sea level. What is the value of ?
Details and assumptions
If the moon moves from the opposite side of the earth from you (A in the above figure) to the facing side (B in the above figure), approximately by what percent does the moon's gravitational force on you (with mass ) increase, assuming that the earth-moon (center-to-center) distance is and the earth's radius is
Assume that the earth and the moon are both perfect spheres and the earth-moon distance is constant.
If the magnitude of gravitational attraction force between two particles with respective masses and is what is the approximate separation between the two particles, given that the universal gravitational constant is
A neutron star has a mass equal to that of the sun, which is but has a radius of only What is the approximate gravitational acceleration at the surface of the star?
Assumptions and details
The interior structure of the Earth is layered in spherical shells, like an onion. Assume that a certain planet has similar interior structure of core and outer shell, as shown in the above figure. The radius of the core is and the inner and outer radii of the outer shell are and respectively. If the mass of the core is and that of the outer shell is what is the approximate gravitational acceleration of a particle which is at a distance of from the surface of the outer shell?