Calculating Speed & Time of Message Packet Through Earth's Center

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SUMMARY

The discussion centers on calculating the speed and time of message packets traveling through a tube bored through the center of a planet with a density of 3820 kg/m³ and a radius of 5.31E+6 m. The gravitational acceleration at a radius r inside the planet is described by the equation d²r/dt² = -g(r). To determine the speed of the message packet at a distance of 0.480R from the center, one must apply principles of gravitational physics and motion. The time taken for a message to traverse from one side of the planet to the other can be calculated using these principles.

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zhenyazh
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Hi,
i am preparing for a test and i really have no idea how to solve the following question.
i would appreciate if some one could give me the direction of solution explaining why things should be done the way the should. i am really clueless here.

The residents of a small planet have bored a hole straight through its center as part of a communications system. The hole has been filled with a tube and the air has been pumped out of the tube to virtually eliminate friction. Messages are passed back and forth by dropping packets through the tube. The planet has a density of 3820 kg/m3, and it has a radius of R=5.31E+6 m.

What is the speed of the message packet as it passes a point a distance of 0.480R from the center of the planet?

How long does it take for a message to pass from one side of the planet to the other?

thanks
 
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Hi zhenyazh! :smile:

What is the gravitational acceleration at radius r inside the planet?

If it's g(r), then d2r/dt2 = -g(r). :wink:
 
thanks for your response but i still don't get it.
can u give a more detailed explanantion?
 

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