[FEAT] Add Newton's Law of Gravitation algorithm (#6855)

Co-authored-by: Priyanshu1303d <[email protected]>

Author: Priyanshu1303d

src/main/java/com/thealgorithms/physics/Gravitation.java

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+package com.thealgorithms.physics;
+
+/**
+ * Implements Newton's Law of Universal Gravitation.
+ * Provides simple static methods to calculate gravitational force and circular orbit velocity.
+ *
+ * @author [Priyanshu Kumar Singh](https://github.com/Priyanshu1303d)
+ * @see <a href="https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation">Wikipedia</a>
+ */
+public final class Gravitation {
+
+    /** Gravitational constant in m^3 kg^-1 s^-2 */
+    public static final double GRAVITATIONAL_CONSTANT = 6.67430e-11;
+
+    /**
+     * Private constructor to prevent instantiation of this utility class.
+     */
+    private Gravitation() {
+    }
+
+    /**
+     * Calculates the gravitational force vector exerted by one body on another.
+     *
+     * @param m1 Mass of the first body (kg).
+     * @param x1 X-position of the first body (m).
+     * @param y1 Y-position of the first body (m).
+     * @param m2 Mass of the second body (kg).
+     * @param x2 X-position of the second body (m).
+     * @param y2 Y-position of the second body (m).
+     * @return A double array `[fx, fy]` representing the force vector on the second body.
+     */
+    public static double[] calculateGravitationalForce(double m1, double x1, double y1, double m2, double x2, double y2) {
+        double dx = x1 - x2;
+        double dy = y1 - y2;
+        double distanceSq = dx * dx + dy * dy;
+
+        // If bodies are at the same position, force is zero to avoid division by zero.
+        if (distanceSq == 0) {
+            return new double[] {0, 0};
+        }
+
+        double distance = Math.sqrt(distanceSq);
+        double forceMagnitude = GRAVITATIONAL_CONSTANT * m1 * m2 / distanceSq;
+
+        // Calculate the components of the force vector
+        double fx = forceMagnitude * (dx / distance);
+        double fy = forceMagnitude * (dy / distance);
+
+        return new double[] {fx, fy};
+    }
+
+    /**
+     * Calculates the speed required for a stable circular orbit.
+     *
+     * @param centralMass The mass of the central body (kg).
+     * @param radius The radius of the orbit (m).
+     * @return The orbital speed (m/s).
+     * @throws IllegalArgumentException if mass or radius are not positive.
+     */
+    public static double calculateCircularOrbitVelocity(double centralMass, double radius) {
+        if (centralMass <= 0 || radius <= 0) {
+            throw new IllegalArgumentException("Mass and radius must be positive.");
+        }
+        return Math.sqrt(GRAVITATIONAL_CONSTANT * centralMass / radius);
+    }
+}

src/test/java/com/thealgorithms/physics/GravitationTest.java

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+package com.thealgorithms.physics;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the Gravitation utility class.
+ */
+final class GravitationTest {
+
+    // A small tolerance (delta) for comparing floating-point numbers
+    private static final double DELTA = 1e-9;
+    private static final double G = Gravitation.GRAVITATIONAL_CONSTANT;
+
+    @Test
+    @DisplayName("Test gravitational force between two bodies on the x-axis")
+    void testSimpleForceCalculation() {
+        // Force on body 2 should be F = G*1*1 / 1^2 = G, directed towards body 1 (negative x)
+        double[] forceOnB = Gravitation.calculateGravitationalForce(1.0, 0, 0, 1.0, 1, 0);
+        assertArrayEquals(new double[] {-G, 0.0}, forceOnB, DELTA);
+
+        // Force on body 1 should be equal and opposite (positive x)
+        double[] forceOnA = Gravitation.calculateGravitationalForce(1.0, 1, 0, 1.0, 0, 0);
+        assertArrayEquals(new double[] {G, 0.0}, forceOnA, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test gravitational force in a 2D plane")
+    void test2DForceCalculation() {
+        // Body 1 at (0,0) with mass 2kg
+        // Body 2 at (3,4) with mass 1kg
+        // Distance is sqrt(3^2 + 4^2) = 5 meters
+        double magnitude = 2.0 * G / 25.0; // G * 2 * 1 / 5^2
+        // Unit vector from 2 to 1 is (-3/5, -4/5)
+        double expectedFx = magnitude * -3.0 / 5.0; // -6G / 125
+        double expectedFy = magnitude * -4.0 / 5.0; // -8G / 125
+
+        double[] forceOnB = Gravitation.calculateGravitationalForce(2.0, 0, 0, 1.0, 3, 4);
+        assertArrayEquals(new double[] {expectedFx, expectedFy}, forceOnB, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test overlapping bodies should result in zero force")
+    void testOverlappingBodies() {
+        double[] force = Gravitation.calculateGravitationalForce(1000.0, 1.5, -2.5, 500.0, 1.5, -2.5);
+        assertArrayEquals(new double[] {0.0, 0.0}, force, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test circular orbit velocity with simple values")
+    void testCircularOrbitVelocity() {
+        // v = sqrt(G*1/1) = sqrt(G)
+        double velocity = Gravitation.calculateCircularOrbitVelocity(1.0, 1.0);
+        assertEquals(Math.sqrt(G), velocity, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test orbital velocity with real-world-ish values (LEO)")
+    void testEarthOrbitVelocity() {
+        // Mass of Earth ~5.972e24 kg
+        // Radius of LEO ~6,771,000 m (Earth radius + 400km)
+        double earthMass = 5.972e24;
+        double leoRadius = 6.771e6;
+        // FIX: Updated expected value to match the high-precision calculation
+        double expectedVelocity = 7672.4904;
+
+        double velocity = Gravitation.calculateCircularOrbitVelocity(earthMass, leoRadius);
+        assertEquals(expectedVelocity, velocity, 0.0001); // Use a larger delta for big numbers
+    }
+
+    @Test
+    @DisplayName("Test invalid inputs for orbital velocity throw exception")
+    void testInvalidOrbitalVelocityInputs() {
+        assertThrows(IllegalArgumentException.class, () -> Gravitation.calculateCircularOrbitVelocity(0, 100));
+        assertThrows(IllegalArgumentException.class, () -> Gravitation.calculateCircularOrbitVelocity(-1000, 100));
+        assertThrows(IllegalArgumentException.class, () -> Gravitation.calculateCircularOrbitVelocity(1000, 0));
+        assertThrows(IllegalArgumentException.class, () -> Gravitation.calculateCircularOrbitVelocity(1000, -100));
+    }
+}