Two asteroids with masses m1 and m2 are found in free space, infinitely remote from all other bodies. at the initial moment, the distance between the asteroids is l0 and their velocities are ~v1 and ~v2, oppositely directed along the line connecting their centres, so that the asteroids are moving away from each other. find the maximal distance between the asteroids during their motion.

While standing outdoors one evening, you are exposed to the following four types of electromagnetic radiation: yellow light from a sodium street lamp, radio waves from an am radio station, radio waves from an fm radio station, and microwaves from an antenna of a communications system. rank these type of waves in terms of increasing photon energy.

Two identical stars with mass m orbit around their center of mass. each orbit is circular and has radius r, so that the two stars are always on opposite sides of the circle. (a) find the gravitational force of one star on the other. (b) find the orbital speed of each star and the period of the orbit. (c) how much energy would be required to separate the two stars to infinity?

Consider a small frictionless puck perched at the top of a fixed sphere of radius r. if the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [hint: use conservation of energy to find the puck's speed as a func e conservation of energy to find the puck's speed as a function of its height at what value of this normal force does the puck leave the sphere? ] here on the puck.