Understanding the Concepts

* Weight: Weight is the force of gravity acting on an object's mass. It's calculated using the formula: Weight (W) = Mass (m) * Acceleration due to gravity (g)

* Gravity: The acceleration due to gravity (g) depends on the planet's mass (M) and radius (R): g = GM/R² (where G is the gravitational constant).

Solving the Problem

1. Find the person's mass:

* We know their weight on Earth is 800 N.

* Earth's acceleration due to gravity is approximately 9.8 m/s².

* Using the weight formula: 800 N = m * 9.8 m/s²

* Solving for mass: m = 800 N / 9.8 m/s² ≈ 81.6 kg

2. Calculate the new gravity:

* The other planet has twice the mass (2M) and twice the radius (2R) of Earth.

* New gravity (g') = G(2M) / (2R)² = (1/2) * (GM/R²)

* Since g = GM/R², we have g' = (1/2) * g

* Therefore, the new gravity is half the gravity on Earth: g' = (1/2) * 9.8 m/s² = 4.9 m/s²

3. Calculate the person's weight on the new planet:

* Weight on new planet (W') = Mass (m) * New gravity (g')

* W' = 81.6 kg * 4.9 m/s² ≈ 400 N

Answer: The person's weight on the other planet is most nearly 400 Newtons.