Gravity/Planetary Forces Question - High School physics question

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Homework Help Overview

The discussion revolves around a physics problem related to gravitational forces, specifically determining the distance at which an object can be placed between the Earth and the Sun to achieve a state of balance where it does not move. The context involves understanding gravitational interactions and equilibrium conditions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to set the gravitational forces from the Earth and the Sun equal to each other to find the balance point. Some participants question the need to substitute a specific mass for the object, suggesting it cancels out in the equations. Others discuss the setup of the equations and the distances involved.

Discussion Status

Participants are actively engaging with the problem, offering hints and clarifications about the approach to equate the gravitational forces. There is a recognition of the need to express the distances correctly in relation to the total distance between the Earth and the Sun. The original poster indicates progress in understanding the problem.

Contextual Notes

There is an emphasis on the assumption that the object is placed along the line connecting the Earth and the Sun, and the discussion includes the gravitational constant and the masses of the celestial bodies involved. The problem is framed within the constraints of a high school physics homework assignment.

closertolost
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Homework Statement


Find the distance an object needs to be in between the sun and the Earth for it to be perfectly balanced (not moving)

Homework Equations


mass of Earth = 5.98e24 kg
mass of sun=1.991e30 kg
distance between sun and Earth = 1.479e11 m
Fg=Gm1m2/r²

The Attempt at a Solution


well, i tried making the Fg zero for two equations - one with Fg of the object to the sun, and one with Fg of the object to the earth..but it got messed up..can someone help me?

can i sub in the mass of the object as 1kg?
 
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Hint: The point at which the object won't accelerate is the point at which the gravitational forces on the object are *equal* in magnitude (and opposite in direction).

No, you don't need to substitute in a numerical value for the mass of the object, because it should cancel from both sides of the equation (meaning that the point at which the forces balance doesn't depend upon how heavy the object is).
 
so, do i put
Fg=(6.67e-11 x 5.97e24)/d²
Fg=(6.67e-11kg x 1.991e30kg)/1.479e11m-d² <---because d is the distance to the object, and 1.479e11 is the distance from sun to Earth (?)
 
oh, and then cram the equations together :P
 
closertolost

When I hinted that the gravitational forces on the object due to Earth and the sun were equal, I meant for you to actually *equate* them. So, using the subscripts E and S for Earth and sun respectively, we have:

FE = FS

GmME/r2 = GmMS/(R-r)2

You'll notice I've done something interesting here with the distances. I've decided to call the distance between the Earth and the sun "R." So, if the object is a distance r from Earth, then its distance from the sun must necessarily be R-r (since the problem states that the object lies along a straight line connecting the two celestial bodies). If you're still not sure, draw a diagram. EDIT: I see that you already figured this out, nice work.

You'll also notice that m, the mass of the "test object" cancels from both sides of the equation, and so does the gravitational constant, G. This leaves you with an equation for r (the thing you are trying to calculate) in terms of three known quantities. The three known quantities are the masses of the Earth and sun, and the Earth-sun distance, R.
 
ahah thanks very much! i have it now :)
 

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