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Planet #2 (mass M2) and planet #3 (mass M3) are separated by distance R. Planet #1 (mass M1) is directly between these two planets. If M3 = 25 M2 and R=20, then what is the value of r such that the total force on planet #1 is zero?

Planet #2 (mass M2) and planet #3 (mass M3) are separated by distance R. Planet #1 (mass M1) is directly between these two planets. If M3 = 25 M2 and R=20, then what is the value of r such that the total force on planet #1 is zero?

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Planet #2 (mass M2) and planet #3 (mass M3) are separated by distance R. Planet #1 (mass M1) is directly between these two planets.
If M3 = 25 M2 and R=20, then what is the value of r such that the total force on planet #1 is zero?

### Description of Diagram: Planetary Forces This diagram illustrates the gravitational interaction between three planets, labeled as Planet #1, Planet #2, and Planet #3. - **Planet #1 (M₁):** - Represented by a small green circle. - Positioned between Planet #2 and Planet #3 on a dotted line. - **Planet #2 (M₂):** - Depicted as a small blue circle. - Located to the right of Planet #1. - **Planet #3 (M₃):** - Shown as a larger red circle. - Positioned to the left of Planet #1. ### Distances and Direction of Forces: - **Distance (r):** - This is the distance between Planet #1 and Planet #2. - A double-headed arrow labeled "r" indicates this distance. - **Distance (R):** - Indicates the distance between Planet #1 and Planet #3. - Represented by a longer double-headed arrow across the dotted line. ### Forces: - Arrows are shown pointing towards and away from each planet, indicating the gravitational forces acting along the line connecting the three planets. The forces are implicitly understood to be acting along these distances due to the gravitational attraction between the planetary masses \( M_1 \), \( M_2 \), and \( M_3 \). This diagram helps in understanding the gravitational attraction and distances in a system of three planets aligned in a straight line.
Transcribed Image Text:### Description of Diagram: Planetary Forces This diagram illustrates the gravitational interaction between three planets, labeled as Planet #1, Planet #2, and Planet #3. - **Planet #1 (M₁):** - Represented by a small green circle. - Positioned between Planet #2 and Planet #3 on a dotted line. - **Planet #2 (M₂):** - Depicted as a small blue circle. - Located to the right of Planet #1. - **Planet #3 (M₃):** - Shown as a larger red circle. - Positioned to the left of Planet #1. ### Distances and Direction of Forces: - **Distance (r):** - This is the distance between Planet #1 and Planet #2. - A double-headed arrow labeled "r" indicates this distance. - **Distance (R):** - Indicates the distance between Planet #1 and Planet #3. - Represented by a longer double-headed arrow across the dotted line. ### Forces: - Arrows are shown pointing towards and away from each planet, indicating the gravitational forces acting along the line connecting the three planets. The forces are implicitly understood to be acting along these distances due to the gravitational attraction between the planetary masses \( M_1 \), \( M_2 \), and \( M_3 \). This diagram helps in understanding the gravitational attraction and distances in a system of three planets aligned in a straight line.
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