How long until the planets collide?

AI Thread Summary
The discussion focuses on calculating the time until two planets collide, given their masses, radii, initial distance, and angular velocity. The user has established a free-body diagram and noted that the center of mass remains constant due to the absence of external forces. They are struggling to set up the necessary differential equations for the problem. Another participant suggests that the collision scenario requires considering dissipative forces, such as friction, to account for energy loss. The conversation emphasizes the need for a more complex approach to model the planets' interactions accurately.
jgens
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Homework Statement



Two planets of masses m_1 and m_2 with radii r_1 and r_2 respectively are orbiting their common center of mass at some initial distance x_0 from each other with angular velocity \omega_0. Find the amount of time it takes for these planets to collide.

Homework Equations



N/A

The Attempt at a Solution



So far, I've drawn my free-body diagram with the axes in the Center of Mass reference frame, figured that the position of the center of mass remains constant since no net external force acts, and that conservation of momentum applies since no net external torque acts either. However, I'm having difficulty setting the problem up (constructing a series of differential equations to solve) and would appreciate any advice.

Thanks!
 
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jgens said:
Find the amount of time it takes for these planets to collide.
Thanks!
Hello jgens
In the way you put it it is a potential equation. For colliding you need something diffusive. Rotational energy diminishing because of friction or any other diffusion. For instance if a speaker moves particles a comoving for some time, that is called sound. Since this comovement diffuses the sound deminishes and the particles are moving statistically erradic again.
greetings Janm
 

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