Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 month ago

Do masses accelerate in the universal law of gravitation?

We know F = GMm/d^2. As “F” is inversely proportional to on-center distance “d” between M and m, therefore, both “M” and “m” should start to decelerate upon the reduction in constant F on either side but it is said they both accelerate towards each other [gravitational force “F” decreases when on-center distance “d” decreases] - Any reasons.

Update:

F reduces but it doesn't vanish. Masses are still under the constant application of gravitational force 

Update 2:

Sorry i messed up with my question

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  • 1 month ago
    Favorite Answer

    No, F is inversely proportional to the square of the distance.

    the rest of your question makes zero sense.  The "therefore" does not follow.

    "“M” and “m” should start to decelerate" why would they even move. If they were free to move, they would accelerate towards each other, 

    troll....

  • 1 month ago

    You said “F” decreases when on-center distance “d” decreases] 

    and

    F reduces but it doesn't vanish. Not much has been said yet about that error. 

    When distance d decreases, the force F increases. That's the way inversely proportional works.

    Source(s): Newton fan for years.
  • 1 month ago

    I suggest you enrol for a physics course.  You may be able to formulate a sensible question in a year or two.

  • Anonymous
    1 month ago

     Are you a troll?  What you have said is full of mistakes (grammar, physics and logic).  Can't be an accident.

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  • 1 month ago

    You seem to assume F stays constant despite "d" changing.  It does not.  Gravity is an attractive force (or in general relativity the result of the warping of space-time due to the masses).  So if you have two objects of masses M and m respectively, and set them d meters apart they will each experience a force F given by 

    F = GMm/d^2  where G = constant

    Now in the absence of any other force the mass M will accelerate toward m, the acceleration given by:

     F = M*A = GMm/d^2  -->  A = Gm/d^2

    and the mass m accelerates toward M with acceleration  a = GM/d^2.  This is also a consequence of Newton's law - for every action there is an equal and opposite reaction.

    now A, a, and d look like constants but they aren't.  If M and m are moving then we need to represent the accelerations as

    A = d^2X/dt^2   and a = d^2x/dt^2  where X = position of M with respect to center of mass of the system and x = position of M with respect to center ofmass of the system

    d is then d = X - x  so we  need to solve

    d^2X/dt^2 = Gm/(X - x)^2   and d^2x/dt^2 = GM/(X-x)^2

    to find out how X and x change in time.  They should get smaller as the two masses move toward each other which means the force increases with time, as does the acceleration.

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