Solve Gravitation Problem between Earth & Sun

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To find the point between the Earth and the Sun where the net gravitational force on an object is zero, one must use the gravitational force equation F=G(m1m2/r^2). The discussion emphasizes that the distance between the Earth and the Sun is crucial for calculations, as this distance varies. A suggested approach involves setting the gravitational forces from both bodies equal to each other, leading to the equation (y-x)(332943.1438)=x, where y is the distance between the Earth and the Sun and x is the distance of the object from the Sun. By substituting the known values, one can solve for x and subsequently determine the distance from the Earth. Understanding the gravitational dynamics between these two massive bodies is essential for solving this problem.
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Gravitation Problem :(

Question:
Find the point between Earth and the sun at which an object can be placed so that the net gravitational force exerted by Earth and the sun on an object is zero.

Earth's mass: 5.98x10^24 kg
Earth's radius: 6.38x10^6 m

Sun's mass: 1.991x10^30 kg
Sun's radius: 6.96x10^8 m


I know I have to use the equation for gravitational force:
F=G(m1m2/r^2)

So at this point I'm lost. Do I make up a mass for the object and figure out the force for Earth and the sun separately? Do I put the values for the sun and Earth into one equation and set the force equal to zero? Any help would be greatly appreciated :D
 
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take any arbitrary mass m and go from there.
 
So I found the sun and the Earth's respective gravitational forces...
How would I go about finding the point where they equal zero?
 
Show us your calculations.
 


this question is complete, for this you should must knew about the distance between sun and earth...
as this distance keeps changes therefore first notify the exact distance for which you want the answer.ok
well according to me ans should be
(y-x)(332943.1438)=x

where y means distance between Earth and sun

and x means distance of object from sun...
therefore after putting value of "y" you will get value of "x" and after it you can easily find distance between object and Earth too
 

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