\(\mathbf{T} / \mathbf{F}:\) In a binary system, the more massive star moves more slowly than the less massive star.

Newton's law of gravitation is fundamental to understanding the behavior of stars in a binary system. This law states that any two objects with mass attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force is described with the equation:

\[ F = G \frac{m_1 m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between the centers of the two masses.

In a binary star system, both stars exert gravitational forces on each other, which keeps them in orbit around their common center of mass. Due to this gravitational attraction, we can predict and explain how stars move relative to one another.

Kepler's third law is crucial in understanding the relationship between the orbital period and the orbit size of stars in a binary system. This law states that the square of the orbital period (\( T \)) of any planet (or star) is proportional to the cube of the semi-major axis (\( a \)) of its orbit:

\[ T^2 \, \propto \, a^3 \]
This means that if you know the size of the orbit (semi-major axis), you can determine the orbital period, and vice versa.

When applied to binary systems, this law helps us understand why a star with a larger orbit (the less massive star) moves faster compared to its heavier partner with a smaller orbit. The star with the larger orbit must maintain a higher speed to balance the gravitational force and keep the system stable. In other words, the orbital velocity for a star in a binary system is higher if its orbit radius is larger.

In a binary star system, both stars orbit around a common center of mass. The center of mass is the point where the masses of the system balance each other. The more massive star will be closer to this center of mass, while the less massive star will be further away.

Understanding the center of mass is essential because it explains the relative motions of the stars. The position of the center of mass can be calculated using the equation:

\[ R_{cm} = \frac{m_1 r_1 + m_2 r_2}{m_1 + m_2} \]
where \( R_{cm} \) is the distance to the center of mass, \( m_1 \) and \( m_2 \) are the masses of the two stars, and \( r_1 \) and \( r_2 \) are their distances from the center of mass.

Since the more massive star is closer to the center of mass, it has a smaller orbit radius and thus moves more slowly. In contrast, the less massive star, being farther from the center of mass, travels a larger distance in the same period and hence moves faster.