If the Sun's mass were reduced by half, its gravitational force would also change accordingly. The gravitational force \( F \) between two objects is described by Newton's law of universal gravitation, which states:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two objects.
If we assume that \( m_1 \) is the mass of the Sun (which we are halving), then the gravitational force acting on an object (like a planet) due to the Sun would also be halved, assuming that the distance \( r \) from the center of the Sun to the object remains constant.
Specifically, if the Sun's mass goes from \( M \) to \( \frac{M}{2} \), the gravitational force \( F \) would also be halved:
\[ F' = \frac{G \cdot \left( \frac{M}{2} \right) \cdot m_2}{r^2} = \frac{1}{2} \left( \frac{G \cdot M \cdot m_2}{r^2} \right) = \frac{F}{2} \]
Thus, if the Sun's mass were reduced by half, the gravitational force that it exerts on the planets would also be reduced by half. This reduction in gravity would affect the orbits of the planets, potentially causing them to move away from the Sun or alter their orbital characteristics.
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