Ackbach said:To me it seems as if you have to balance the potential energy due to gravity against the rotational kinetic energy. That is, it seems as if you're in outer space with two equal masses, and they are rotating around each other like a binary star system. If the distance between them is constant, how fast are they rotating around each other?
dwsmith said:Fast enough to not be pulled in by the others gravity and a slow enough that they don't fly off.
dwsmith said:Is this question talking about the position vector for the center of gravity of the two bodies?
If we set the origin to be the center of gravity, the bodies orbit it in a uniform circle with radius 1/2r_0.
I can just find the angular velocity on this circle?
A relative position vector is a mathematical representation of the position of an object relative to a reference point. It is used to describe the location of an object in a specific coordinate system.
While both relative position and displacement vectors describe the location of an object, they differ in that displacement vectors only consider the change in position from one point to another, while relative position vectors take into account the position of the object relative to a reference point at a specific moment in time.
A relative position vector includes both magnitude and direction. The magnitude is the distance from the reference point to the object, while the direction is the angle at which the object is located from the reference point.
A relative position vector is typically represented by an arrow pointing from the reference point to the object. It can also be represented by its components in the x, y, and z directions.
A relative position vector can be calculated using the Pythagorean theorem and trigonometric functions. The magnitude can be found by taking the square root of the sum of the squares of the x, y, and z components, and the direction can be determined using trigonometric ratios.