1. Let's start by stating the problem: We want to understand the formulas for gravity according to Newton and Einstein. 2. Newton's law of universal gravitation states that the force between two masses is given by the formula: $$F = G \frac{m_1 m_2}{r^2}$$ where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers. 3. This formula tells us that the force is directly proportional to the product of the masses and inversely proportional to the square of the distance between them. 4. Einstein's theory of gravity is described by General Relativity, which replaces the Newtonian force with the concept of spacetime curvature. 5. The key equation in Einstein's gravity is the Einstein field equation: $$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu}$$ where $G_{\mu\nu}$ is the Einstein tensor describing spacetime curvature, $\Lambda$ is the cosmological constant, $g_{\mu\nu}$ is the metric tensor, $T_{\mu\nu}$ is the stress-energy tensor, $G$ is the gravitational constant, and $c$ is the speed of light. 6. This equation shows how matter and energy ($T_{\mu\nu}$) influence the curvature of spacetime ($G_{\mu\nu}$), which we perceive as gravity. 7. In summary, Newton's formula gives a force between masses, while Einstein's formula describes gravity as geometry of spacetime influenced by mass-energy. Final answers: Newton's gravity formula: $$F = G \frac{m_1 m_2}{r^2}$$ Einstein's gravity formula (Einstein field equation): $$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu}$$