Oscillation in Space: Derive an Equation to Determine Period in Years

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The discussion focuses on deriving an equation to determine the period of oscillation for a third mass placed between two equal masses in space. The two masses, each 2.1 solar masses and separated by 8.4 AU, create a gravitational field that influences the third mass when it is displaced vertically. The motion of the third mass is approximated as simple harmonic due to the gravitational forces acting on it. Participants are encouraged to share their attempts and specific challenges faced in the derivation process. The goal is to arrive at a formula that expresses the period of oscillation in years.
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In the middle of empty space two equal masses, M = 2.1 solar masses, lie fixed on a horizontal line separated by a distance D = 8.4 AU. Halfway between the masses lies a third mass. The third mass is displaced vertically a distance y where y << D. Due to the gravitational attraction from the other two masses, the third mass will be pulled back toward the line. The subsequent motion of the third mass will be approximately simple harmonic. Determine the period of the motion in years.


Please derive a equation to solve this problem
 
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Hi xgoodtimesx! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 

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