Angular acceleration of a planet

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Discussion Overview

The discussion revolves around the concept of angular acceleration in the context of a planet's motion in a star-planet system. Participants explore the relationship between distance from the center of mass, centripetal acceleration, and the forces involved in orbital mechanics. The scope includes theoretical considerations and conceptual clarifications related to gravitational forces and motion.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants question how an object farther from the center can experience greater centripetal acceleration, given that gravitational force decreases with distance according to the formula F = GmM/r^2.
  • Others assert that a planet farther from the star would have smaller centripetal acceleration because it moves slower in its orbit, requiring less speed to maintain that orbit.
  • A participant emphasizes the distinction between speed and velocity in the context of circular motion, noting that acceleration is the change in velocity over time.
  • Some participants express doubts about whether planets are the appropriate example for discussing these concepts, particularly regarding the constancy of the period of circular motion.
  • A reference to a related homework help thread is provided for further exploration of the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus; there are multiple competing views regarding the relationship between distance, centripetal acceleration, and gravitational forces in planetary orbits.

Contextual Notes

There are unresolved assumptions regarding the applicability of the textbook examples to real planetary systems, particularly concerning the constancy of orbital periods and the nature of gravitational orbits.

itachipower
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So my teacher said that an object farther from the center experiences greater centripetal acceleration. How is that possible? let's say we have a sun + planet system. F = GmM/r^2 so when the planet's r is greater, wouldn't the force become lower compared to the planet being closer to the sun?
 
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When the planet's r is greater... the fource would become lower compared to the planet being FARTHER from the sun.

Also, call it star, not Sun. The Sun is our star
 
gabriel.dac said:
When the planet's r is greater... the fource would become lower compared to the planet being FARTHER from the sun.

Also, call it star, not Sun. The Sun is our star

What if it was a ball attached to a string? How would that be different from a binary planet-star system?
 
itachipower said:
What if it was a ball attached to a string? How would that be different from a binary planet-star system?

The planet would have smaller centripetal acceleration because it would be moving slower than if it was closer to the Sun. It needs less speed to stay in orbit
 
gabriel.dac said:
The planet would have smaller centripetal acceleration because it would be moving slower than if it was closer to the Sun. It needs less speed to stay in orbit

Speed isn't a proper term in physics. In the case of circular motion, it's velocity that represents both (1) the rate of motion and (2) the direction.

Acceleration, on the other hand, is the change in velocity over time. Which is constantly changing direction in circular motion, albeit uniformly.

PF indicates a larger orbit will have a larger centripetal acceleration. See thread link in my next post.
 
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itachipower said:
So my teacher said that an object farther from the center experiences greater centripetal acceleration. How is that possible? let's say we have a sun + planet system. F = GmM/r^2 so when the planet's r is greater, wouldn't the force become lower compared to the planet being closer to the sun?

Your teacher is correct. Physics Forum indicates so in a planetary example, but I'm wondering if planet's orbits are a proper example.

I'm having some doubts about the OP question - if planets are the example the textbook had in mind. If the period of the circular motion stays constant, the acceleration is obviously greater the further from the center. But gravitational orbits...

There's a homework help thread on this exact question here:
www.physicsforums.com/showthread.php?t=548403

Hope a PF expert will reply and help sort this out.
 
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