What is the proportionality constant for the Sun's gravitational force?

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Discussion Overview

The discussion revolves around the gravitational force exerted by the Sun on planets, specifically focusing on the proportionality constant involved in this relationship. Participants explore the theoretical underpinnings of gravitational force in the context of orbital mechanics.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant references a book stating that the gravitational pull of the Sun is proportional to a planet's mass divided by its orbital radius, seeking clarification on the proportionality constant.
  • Another participant suggests that for an object in orbit, the centrifugal force must equal the gravitational force, implying a balance of forces in orbital mechanics.
  • A different participant proposes using the formula F=(4pi^2mr)/T^2 as relevant to the discussion of gravitational forces in orbits.
  • One participant reiterates the relationship, stating that the gravitational pull is proportional to the planet's mass divided by the square of its orbital radius, providing the formula F_g = G(M_sun M_planet)/r_orbit^2 and mentioning the gravitational constant G.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between gravitational force and orbital mechanics, with no consensus reached on the correct proportionality constant or the appropriate formula to use.

Contextual Notes

Some statements depend on specific definitions of gravitational force and orbital mechanics, and there are unresolved aspects regarding the application of different formulas in this context.

moonman239
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This book that I'm reading mentions something where the gravitational pull of the Sun is proportional to that planet's mass/its orbital radius. What is this proportionality constant?
 
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Not quite , for an object in orbit the centrifugal force throwing it outwards is equal to the gravitational force pulling it into the object in the centre.
 
Oh, okay. So really, F=(4pi^2mr)/T2 should be used.
 
moonman239 said:
This book that I'm reading mentions something where the gravitational pull of the Sun is proportional to that planet's mass/its orbital radius. What is this proportionality constant?

The gravitational pull on any planet by the Sun is proportional to that planet's mass divided by the square of its orbital radius. The actual formula is

[tex]F_g = G\frac{M_{sun}M_{planet}}{r_{orbit}^2}[/tex]

where G is the gravitational constant and is equal to 6.673e-11 when M is measured in Kg and r in meters.
 

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