How would the tidal forces change if you reduced the distance between two objects by one half?
-1/3 as strong
-1/8 as strong
-3 times stronger
-8 times stronger
I believe it would be 8 times stronger, but I never trust my own math. A second opinion would be appreciated!
-1/3 as strong
-1/8 as strong
-3 times stronger
-8 times stronger
I believe it would be 8 times stronger, but I never trust my own math. A second opinion would be appreciated!
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You're right -- 8 times stronger.
Tidal force varies inversely with the third power of distance (unlike gravitational force, which varies inversely with the second power of distance). That's why the moon exerts such a strong tidal force on the earth, even though it is far less massive than the sun. If you moved the moon halfway towards the earth, its tidal force would be 8 times greater.
(Mathematical aside: The tidal force of an object on earth is the difference between its gravitational force on the near side of earth and its force on the far side. That is, tidal force is a difference between gravitational forces. Mathematically, this is equivalent to a derivative. Gravity is proportional to 1/R^2, and the derivative of this is proportional to 1/R^3.)
Tidal force varies inversely with the third power of distance (unlike gravitational force, which varies inversely with the second power of distance). That's why the moon exerts such a strong tidal force on the earth, even though it is far less massive than the sun. If you moved the moon halfway towards the earth, its tidal force would be 8 times greater.
(Mathematical aside: The tidal force of an object on earth is the difference between its gravitational force on the near side of earth and its force on the far side. That is, tidal force is a difference between gravitational forces. Mathematically, this is equivalent to a derivative. Gravity is proportional to 1/R^2, and the derivative of this is proportional to 1/R^3.)
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4 times stronger. (2r)^2 = 4 r^2= 1/ FGMm