Universal Gravitation - A Scale Model?

📌 CONCEPT: The universal law of gravitation can be applied to scale models of the solar system to ensure that the gravitational force between the Earth and the Sun remains the same in both the real and the model system.

📐 RULE / FORMULA: According to the universal law of gravitation, the gravitational force between two bodies is given by F = G (m1m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between their centers.

💡 WORKED EXAMPLE: Given that the mass of the Earth is 6 x 10^24 kg, the radius is 6.37 x 10^6 m, and the diameter of the Sun is 1 m, we need to find the radius of the scale model. Let's assume the mass of the Sun is 1.99 x 10^30 kg. Since the diameter of the Sun in the model is 1 m, the radius is 0.5 m. We can now use the formula to find the radius of the scale model, r = (G (m1m2) / F)^(1/2), where F is the gravitational force between the Earth and the Sun in the real system.

⚠️ COMMON MISTAKE: Students often forget to maintain the same gravitational force between the Earth and the Sun in both the real and the model system, leading to incorrect scale models.