Gravitational Field Strength at a Distance?

📌 CONCEPT: The gravitational field strength at a distance from the center of a planet is given by the formula: gravitational field strength = G × mass of the planet / distance^2, where G is the gravitational constant.

📐 RULE / FORMULA: The gravitational field strength is inversely proportional to the square of the distance from the center of the planet. We can use the formula: (G1 / G2) = (R1^2 / R2^2), where G1 and G2 are the gravitational field strengths at distances R1 and R2 from the center of the planet.

💡 WORKED EXAMPLE: Given: G1 = 3 N/kg at R1 = 2R, R2 = 4R. We need to find G2. Using the formula, we have: (G1 / G2) = (R1^2 / R2^2) = (4R^2 / 4^2R^2) = (1/4). Rearranging, G2 = 4G1 = 4(3 N/kg) = 12 N/kg.

⚠️ COMMON MISTAKE: Students often forget to square the distances in the formula and get the wrong answer.