Newton's law of gravity can indeed be considered as a special case of Einstein's general theory of relativity. While the two theories have different formulations and underlying principles, they are equivalent in certain situations where gravitational fields are weak and velocities are much smaller than the speed of light.
Newton's law of gravity, formulated by Sir Isaac Newton in the 17th century, describes the gravitational interaction between two masses. It states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law works well for everyday situations and is still widely used in many practical applications.
Einstein's general theory of relativity, developed in the early 20th century, provides a more comprehensive and accurate description of gravity. It formulates gravity as the curvature of spacetime caused by the presence of mass and energy. In this theory, the motion of objects is determined by the curvature of spacetime, rather than a force acting at a distance.
In the limit of weak gravitational fields and low velocities, the predictions of general relativity converge with those of Newton's law of gravity. This means that in scenarios where gravitational effects are not extremely strong (such as in our everyday experiences), the equations of general relativity simplify and reduce to the familiar equations of Newton's law of gravity.
Therefore, while the two theories have different mathematical formulations and conceptual foundations, they are considered equivalent in situations where the effects of general relativity are negligible, and Newton's law of gravity provides accurate results. However, in cases involving strong gravitational fields, high velocities, or situations where precise measurements are required (e.g., GPS systems or astrophysical phenomena), the predictions of general relativity diverge significantly from those of Newtonian gravity, and the more comprehensive theory is necessary for accurate calculations.