This calculator helps you determine the gravitational force between two objects based on their masses and the distance between their centers.
Inputs
kilograms (kg)
kilograms (kg)
meters (m)
Gravitational Force: — Newtons (N)
Understanding Gravitational Force (F.g.)
Gravitational force is a fundamental attractive force that exists between any two objects with mass. It's the force that keeps planets in orbit around stars, holds galaxies together, and causes objects to fall to the ground when dropped. The strength of this force depends on the masses of the objects involved and the distance separating them.
Newton's Law of Universal Gravitation
The mathematical relationship describing gravitational force was formulated by Sir Isaac Newton and is known as the Law of Universal Gravitation. It states that:
The gravitational force (Fg) between two objects is directly proportional to the product of their masses (m1 and m2).
The gravitational force (Fg) is inversely proportional to the square of the distance (r) between their centers.
This relationship is expressed by the following formula:
Fg = G * (m1 * m2) / r2
Explanation of Terms:
Fg: The gravitational force, measured in Newtons (N).
G: The gravitational constant. This is a fundamental constant of nature, representing the strength of gravity itself. Its accepted value is approximately 6.674 × 10-11 N⋅m2/kg2.
m1: The mass of the first object, measured in kilograms (kg).
m2: The mass of the second object, measured in kilograms (kg).
r: The distance between the centers of the two objects, measured in meters (m).
How to Use the Calculator:
Mass of Object 1 (kg): Enter the mass of the first object in kilograms. This could be a planet, star, or any other object with mass. Use scientific notation (e.g., 5.972e24 for Earth's mass).
Mass of Object 2 (kg): Enter the mass of the second object in kilograms.
Distance Between Centers (m): Enter the distance between the centers of the two objects in meters. For celestial bodies, this is typically the distance between their centers of mass.
Calculate Force: Click the "Calculate Force" button.
The calculator will then output the calculated gravitational force in Newtons (N).
Examples:
Example 1: Earth and the Moon
Mass of Earth (m1): 5.972 × 1024 kg
Mass of Moon (m2): 7.342 × 1022 kg
Average Distance (r): 3.844 × 108 m
Using the calculator with these values will approximate the gravitational force between the Earth and the Moon, which is crucial for understanding lunar orbits and tides.
Example 2: Two Average-Sized Humans
Mass of Person 1 (m1): 70 kg
Mass of Person 2 (m2): 60 kg
Distance (r): 1 meter
This example highlights how incredibly weak gravity is at everyday scales. The force calculated will be minuscule, demonstrating why we don't feel the gravitational pull between people directly.
Applications:
This calculator is useful for:
Students learning about physics and Newton's Law of Gravitation.
Astrophysicists and astronomers estimating gravitational interactions between celestial bodies.
Understanding the fundamental forces governing the universe.
function calculateGravitationalForce() {
var G = 6.674e-11; // Gravitational constant in N m^2 / kg^2
var mass1Input = document.getElementById("mass1");
var mass2Input = document.getElementById("mass2");
var distanceInput = document.getElementById("distance");
var forceValueDisplay = document.getElementById("forceValue");
var mass1 = parseFloat(mass1Input.value);
var mass2 = parseFloat(mass2Input.value);
var distance = parseFloat(distanceInput.value);
// Input validation
if (isNaN(mass1) || isNaN(mass2) || isNaN(distance)) {
alert("Please enter valid numbers for all inputs.");
forceValueDisplay.textContent = "Invalid Input";
return;
}
if (mass1 <= 0 || mass2 <= 0) {
alert("Masses must be positive values.");
forceValueDisplay.textContent = "Invalid Input";
return;
}
if (distance <= 0) {
alert("Distance must be a positive value.");
forceValueDisplay.textContent = "Invalid Input";
return;
}
// Calculate gravitational force
var force = G * (mass1 * mass2) / (distance * distance);
// Display the result, formatted to scientific notation for large/small numbers
if (force 0) { // If force is very small, use scientific notation
forceValueDisplay.textContent = force.toExponential(3);
} else if (force >= 1e6) { // If force is very large, use scientific notation
forceValueDisplay.textContent = force.toExponential(3);
}
else {
forceValueDisplay.textContent = force.toFixed(6); // Standard decimal for intermediate values
}
}