Does Planet Mass Affect Orbital Period?

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Discussion Overview

The discussion centers on the relationship between planet mass and its orbital period, exploring whether a more massive planet requires a greater velocity to maintain equilibrium in its orbit. Participants reference gravitational forces and orbital mechanics, considering both theoretical and practical implications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that the orbital period of a planet is influenced by its velocity and distance from the star, as well as the mass of the star.
  • Others question whether the mass of the planet itself affects its orbital characteristics, suggesting that a more massive planet might need a greater velocity to maintain equilibrium.
  • One participant notes that while the gravitational force depends on the mass of the planet, the effect of that force is countered by the planet's mass, leading to the conclusion that orbits are generally independent of planet mass unless the planet's mass is significant compared to the star's mass.
  • Another participant argues that if planet mass were a significant factor, larger structures like the ISS would not be feasible to dock with, implying that mass does not influence orbital velocity in practical scenarios.
  • Some participants emphasize that the relationship holds true primarily when the mass of the star is much larger than that of the planet, suggesting that when the masses are comparable, the orbital period is affected by both masses.
  • A later reply clarifies that the distance used in gravitational calculations may differ from the distance to the center of mass in a two-body system, adding complexity to the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the influence of planet mass on orbital period, with some asserting it is negligible under certain conditions, while others argue that it becomes significant when the masses are comparable. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants acknowledge that the assumptions regarding mass ratios and the definitions of distance in gravitational calculations may affect the conclusions drawn. There is also an indication that practical examples, like the ISS, may complicate theoretical models.

Johnnyallen
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I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in.
Question: Is the mass of the planet also a factor? In other words, does a more massive planet have to have a greater velocity to maintain equilibrium?
 
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Johnnyallen said:
I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in.
Question: Is the mass of the planet also a factor? In other words, does a more massive planet have to have a greater velocity to maintain equilibrium?
If you equate the force of gravity, ##F=G\frac{m_{star}m_{planet}}{r^2}## with the force required to produce a circular orbit, ##F=m_{planet}\frac{v^2}{r}##, what happens to the mass of the planet?
 
Johnnyallen said:
I recently read a short summary of Kepler 11 and the Kepler Mission. I understand that the orbital period of a planet is a function of its velocity and distance from the star, and the mass of the star will also factor in.
Question: Is the mass of the planet also a factor? In other words, does a more massive planet have to have a greater velocity to maintain equilibrium?
The force attracting a planet depends on its mass but the effect of that force is divided by that mass so the orbit of planets is independent of their mass. However, if your planet's mass becomes significant, compared with the mass of the star it orbits, then star and planet will orbit around the centre of mass, which could be not near the centre of the star. See this link for some maths on the subject.
 
If the mass of a body were a factor in its orbital velocity we could never have built the ISS.
Once it was larger than a single supply ship, we wouldn't be able to dock with it anymore!
 
jbriggs444 said:
If you equate the force of gravity, ##F=G\frac{m_{star}m_{planet}}{r^2}## with the force required to produce a circular orbit, ##F=m_{planet}\frac{v^2}{r}##, what happens to the mass of the planet?

To be fair, this is only true if M_star is much, much larger than M_planet. If the mass of the orbiting body and of the body being orbited are not dramatically different, then orbital period will absolutely depend on both masses.
 
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cjl said:
To be fair, this is only true if M_star is much, much larger than M_planet. If the mass of the orbiting body and of the body being orbited are not dramatically different, then orbital period will absolutely depend on both masses.
Right, as @sophiecentaur pointed out. This could be understood as the "r" in the gravitational force calculation not being the same as the "r" as in the distance to the center of mass of the two-body system.
 
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