The Gravitational Potential ($V$), also known as the gravitational field potential, is a scalar field representing the work done per unit mass by the gravitational field to bring a test mass from an infinite distance to a specific point in space. It is a fundamental concept in gravitational physics.

The potential is conventionally defined as zero at an infinite distance from the central mass. Since gravity is always an attractive force, bringing a mass closer to the central body requires less external work, hence the potential energy and potential are negative. The closer an object is to the central mass, the more negative the potential becomes.

Significance and Applications:

• Orbital Mechanics: The gravitational potential energy, derived from the potential, is critical for calculating the total mechanical energy of satellites and planets in orbit. This governs the shape and stability of their orbits.
• Escape Velocity: The potential is directly related to the escape velocity—the minimum speed required for an object to escape the gravitational influence of a massive body without further propulsion.
• Astrophysics: It is used to model large-scale structures like galaxies and star clusters, where gravitational forces dictate the movement and distribution of matter. For example, understanding the potential well of a black hole or a neutron star is essential for high-energy astrophysics.

1. Enter the Mass ($M$): In the first input field, enter the Mass of the Central Body (e.g., a planet, star, or satellite) in kilograms ($\text{kg}$). You can use scientific notation (e.g., $5.97e24$ for Earth’s mass).
2. Enter the Distance ($r$): In the second input field, enter the Distance from the Center of the central body to the point of interest, measured in meters ($\text{m}$). The distance must be a positive value.
3. Calculate: Click the “Calculate Gravitational Potential” button.
4. View Results: The tool will display the step-by-step substitution of your values into the formula and provide the final calculated Gravitational Potential ($V$) in $\text{J}/\text{kg}$.