Planet X has a mass of M and a radius of R Planet Y has a mass of 3 M and a radius of 3R. Identical satellites orbit both planets at a distance Rabove their surfaces, as shown above. The planets are separated by such a large distance that the gravitational forces between them are negligible.
How does the gravitational field gx at the surface of Planet X compare with the gravitational field gy at the surface of Planet Y?

Materials will have different energies associated with the electrons inside them. this is related to how strongly bound they are by their work function. if we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. if this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. what is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?