A scientist is studying two moons orbiting a distant planet. The moons are observed to have the same linear velocity and orbital radius. From observations, it is determined that moon A has mass ma : 7.35 × 1022 kg and moon B has mass 13.2 x 1022 kg. If the magnitude of the || gravitational force exerted on moon A is 4.31 × 1020 N, what must be the magnitude of the gravitational force exerted on moon B? You may neglect the mutual gravity of the moons.

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**Title**: Understanding Centripetal Forces in Orbital Motion

**Section**: Dynamics of Centripetal Forces

**Learning Goals**: Explore how centripetal forces affect the motion of celestial bodies.

**Content**:

A scientist is studying two moons orbiting a distant planet. Both moons have the same linear velocity and orbital radius. Observations indicate the following:

- Moon A has a mass \( m_a = 7.35 \times 10^{22} \, \text{kg} \).
- Moon B has a mass \( m_b = 13.2 \times 10^{22} \, \text{kg} \).

The gravitational force exerted on Moon A is measured as \( 4.31 \times 10^{20} \, \text{N} \).

**Problem**: Determine the gravitational force exerted on Moon B, assuming the mutual gravitational attraction between the moons can be neglected.

**Diagram Explanation**:
The diagram depicts a distant planet with two orbiting moons, labeled \( m_a \) and \( m_b \). Dashed lines illustrate their orbital paths around the planet, highlighting their circular orbits.
Transcribed Image Text:**Title**: Understanding Centripetal Forces in Orbital Motion **Section**: Dynamics of Centripetal Forces **Learning Goals**: Explore how centripetal forces affect the motion of celestial bodies. **Content**: A scientist is studying two moons orbiting a distant planet. Both moons have the same linear velocity and orbital radius. Observations indicate the following: - Moon A has a mass \( m_a = 7.35 \times 10^{22} \, \text{kg} \). - Moon B has a mass \( m_b = 13.2 \times 10^{22} \, \text{kg} \). The gravitational force exerted on Moon A is measured as \( 4.31 \times 10^{20} \, \text{N} \). **Problem**: Determine the gravitational force exerted on Moon B, assuming the mutual gravitational attraction between the moons can be neglected. **Diagram Explanation**: The diagram depicts a distant planet with two orbiting moons, labeled \( m_a \) and \( m_b \). Dashed lines illustrate their orbital paths around the planet, highlighting their circular orbits.
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