What is the reasoning behind newton's law of universal gravity?

a.
centripetal force is the force directed toward the center of a circle as a moving object changes direction.

b.
the force any object exerts upon another is related to the distance between them.

c.
the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

An astronaut in space cannot use a scale or balance to weigh objects because there is no gravity. but she does have devices to measure distance and time accurately. she knows her own mass is 77.4 kg , but she is unsure of the mass of a large gas canister in the airless rocket. when this canister is approaching her at 3.50 m/s , she pushes against it, which slows it down to 1.30 m/s (but does not reverse it) and gives her a speed of 2.60 m/s . what is the mass of the canister?