Where is the point of zero gravitational force between Mars and the Sun?

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SUMMARY

The discussion focuses on determining the point of zero gravitational force between Mars and the Sun, where the gravitational forces exerted by both celestial bodies on an object balance each other. The equation derived is Gm0*msun/r^2 = Gm0*mmars/(D-r)^2, which simplifies to msun/r^2 = mmars/(D-r)^2. The user struggles with solving this equation correctly, indicating that the solution involves finding the roots of a quadratic equation. The key takeaway is that proper algebraic manipulation and solving techniques are essential for arriving at the correct answer.

PREREQUISITES
  • Understanding of gravitational force equations, specifically Newton's law of universal gravitation.
  • Familiarity with algebraic manipulation and solving quadratic equations.
  • Knowledge of celestial mechanics, particularly the masses of Mars and the Sun.
  • Basic understanding of the concept of equilibrium in gravitational fields.
NEXT STEPS
  • Review Newton's law of universal gravitation and its applications in celestial mechanics.
  • Practice solving quadratic equations, focusing on methods for finding roots.
  • Explore gravitational equilibrium points in multi-body systems, particularly in astrophysics.
  • Investigate the mass values of Mars and the Sun for accurate calculations in gravitational force problems.
USEFUL FOR

Students and enthusiasts of physics, particularly those studying gravitational forces and celestial mechanics, as well as educators looking for practical examples of gravitational equilibrium in space.

cgotu2
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The problem says to find the point between Mars and the Sun at which an object can be placed so that the net gravitational force exerted by Mars and the Sun on that object is zero.

Here is what I've done so far, but I'm not getting the correct answer:

F(sun) = F(mars)

Gm0*msun/r^2=Gm0*mmars/(D-r)^2

then cancelling out common factors the equation becomes: msun/r^2=mmars/(D-r)^2

D is the separation between Mars and the sun and i have the mass of the sun and mars...so why am i not getting the right answer? Please help!
 
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Just plug in your numbers now..what you've got is fine.
 
I think you need to show us how you actually got to the answer so that we can see were you went wrong. It is actually just solving for the roots of an quadratic equation problem.
 

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