davehatton01 said:A little question: as a planet (such as jupiter) orbits the sun, both the planet, and the sun orbit the same point of the centre of mass. how do you calculate where that centre of mass is?
(2 body problem only)
To calculate the center of mass in a 2-body system, you need to find the individual masses of the two bodies and their respective distances from a fixed point. Then, you can use the formula cm = (m1x1 + m2x2) / (m1 + m2) where cm is the center of mass, m1 and m2 are the masses of the two bodies, and x1 and x2 are their distances from the fixed point.
Calculating the center of mass in a 2-body system allows us to determine the point at which the two bodies have the same amount of mass on either side. This point is important in understanding the motion and stability of the system, as well as in studying the gravitational interactions between the two bodies.
Yes, the center of mass can be outside the physical bodies in a 2-body system. This can happen if the two bodies have significantly different masses or if they are not evenly distributed. In such cases, the center of mass may be closer to the more massive body or even outside of both bodies.
The distribution of mass has a direct impact on the position of the center of mass in a 2-body system. If the masses of the two bodies are evenly distributed, the center of mass will be at the exact midpoint between the two bodies. However, if one body has more mass concentrated towards one end, the center of mass will be closer to that body.
Yes, the center of mass is always a fixed point in a 2-body system, regardless of the motion of the bodies. This is because the center of mass is determined by the masses and distances of the bodies, which do not change unless an external force is applied. However, the position of the center of mass may change if the masses or distances of the bodies change.