Inertial system

Positions, velocities and accelerations must be given relative to some coordinate system, which we call a reference system. A reference system where Newton's second law is exactly valid is called an inertial system.

A reference system fixed in an accelerating train is not an inertial system. A net force is acting on a body in the train, but the acceleration of the body with respect to the train is zero. So Newton's second law is not valid in this reference system.

A reference system S fixed in the Earth is not an inertial system. The Sun and the Moon pull on the Earth, giving the Earth an acceleration which is not present in S, so there is a net force, but no acceleration, thus violating Newton's second law.

In a many-body system, a reference system where the center of mass is at rest or moves with a constant velocity is an inertial system.

The velocities and accelerations shown in Orbit Xplorer are given with respect to a reference system where the center of mass moves with the constant velocity (usually zero) given in Parameters.