The distance of the moon and earth is D the mass of earth is...

The distance of the moon and earth is $D$ the mass of earth is 81 times the mass of moon. At what distance from the center of the earth, the gravitational force will be zero
(A) $\mathrm{D} / 2$
(B) $[(12 \mathrm{D}) / 3]$
(C) $(4 \mathrm{D} / 3)$
(D) $(9 \mathrm{D} / 10)$

Key Concepts

Newton's Law of Universal Gravitation

This law states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It forms the foundation for understanding gravitational interactions and is essential for calculating forces between celestial bodies.

Inverse-Square Law

The inverse-square law explains that as the distance between two objects increases, the gravitational force between them decreases in proportion to the square of that distance. This mathematical relationship is critical when determining how gravitational forces balance at various points in a multi-body system.

Gravitational Equilibrium Point

A gravitational equilibrium point, often referred to as a null point or a Lagrange point in more complex scenarios, is a position between two massive bodies where the gravitational pulls from the two bodies cancel out. This concept is used to determine where an object might experience zero net gravitational force, as the individual forces balance each other.

Mass Ratio Effects in Gravitational Fields

The ratio of masses between two interacting bodies greatly influences the location of their equilibrium point. A larger mass exerts a stronger gravitational pull, shifting the balance point closer to the less massive body. This concept is important in analyzing systems where mass differences dictate the dynamics of gravitational forces.

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