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The problem in the image asks about the weight of a robot with a mass of 4280 kg, which weighs 2820 N on planet A. The radius of planet A is given as \( 3.89 \times 10^6 \) m, and the goal is to find the difference in weight (force of gravity) on planet A and planet B, where both planets have the same mass but different radii.

### Approach:

1. **Gravitational Force Formula**:
   \[
   F = \frac{GMm}{r^2}
   \]
   where:
   - \( F \) is the weight (force of gravity),
   - \( G \) is the gravitational constant \( (6.674 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2) \),
   - \( M \) is the mass of the planet,
   - \( m \) is the mass of the object (the robot, 4280 kg),
   - \( r \) is the radius of the planet.

2. **On Planet A**:
   - Given: 
     - Weight \( F_A = 2820 \, \text{N} \),
     - Radius \( r_A = 3.89 \times 10^6 \, \text{m} \).

   From the equation:
   \[
   F_A = \frac{GMm}{r_A^2}
   \]

3. **On Planet B**:
   Since planet B has the same mass as planet A but a different radius, say \( r_B \), the weight on planet B can be found using:
   \[
   F_B = \frac{GMm}{r_B^2}
   \]

4. **Difference in Weight**:
   The difference between the weights on planets A and B is:
   \[
   \Delta F = F_A - F_B
   \]

Do you have the radius for planet B, or should we continue solving for a general case?

Let me know if you'd like me to continue with this setup or add any missing details.

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### 5 Questions for Further Understanding:
1. How does the weight of an object vary with the planet's radius?
2. Why does the robot weigh less on planet A compared to planet B (assuming they have the same mass)?
3. Can you calculate the mass of planet A using the given weight and radius?
4. What is the significance of gravitational force acting on objects?
5. How would the weight change if the radius of planet B were half that of planet A?

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### Tip:
When calculating gravitational force, the key factor affecting weight is the planet's radius, as the force decreases with the square of the radius.

The mass of a robot is 4280 kg. This robot weighs 2820 N on planet A, which has a radius of 3.89 × 10^6 m. What is the difference between the weights (F_A - F_B) on planet A and planet B if both planets have the same mass but different radii?

Explore how to calculate the weight difference of a robot on two planets with the same mass but different radii. This problem uses Newton's Law of Universal Gravitation and applies the formula F = (GMm) / r^2 to determine how weight varies with planetary radius.

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