Acceleration due to gravityDoes acceleration due to gravity increase when an object at a said radius is doubled? Like for instance, if I said the radius of the earth is 5 k m (not to scale obviously) if I doubled that, so 10 k m will acceleration due to gravity double? Or maybe g / 2? Or would the acceleration stay the same no matter distance?

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Acceleration due to gravityDoes acceleration due to gravity increase when an object at a said radius is doubled? Like for instance, if I said the radius of the earth is   5        k    m   (not to scale obviously) if I doubled that, so   10        k    m   will acceleration due to gravity double? Or maybe   g      /    2? Or would the acceleration stay the same no matter distance?

priffEmipsy4i37m · Accepted Answer

The force on a particle of mass   m on the surface of a spherically symmetric mass distribution (the Earth) is  F  =            G      M      m              R      2        ,where   G is a constant,   M is the body mass and   R is the radius of the distribution. By Newton&#039;s second law, that force equals   m  a, where   a is the acceleration of particle   m. As you can see, this acceleration, which we call gravity acceleration, reads  a  =            G      M              R      2        .If you double the radius (keeping the mass   M fixed), acceleration is decreased by a factor of four.

Matilda Webb · Accepted Answer

This depends on exactly what you mean by this.Acceleration due to gravity is given by :  g  =            G      M              r      2      And note that G is a universal constant, M is the mass doing the attracting and r is the distance from the object&#039;s center of mass.Let&#039;s assume you simply move twice as far away as   r, then the gravitational acceleration you feel will be quartered - that power of two !But if you made the Earth twice and big kept it&#039;s density the same - so you filled the extra space, what would happen ?Well :  M  =      4    3    π      r    3    ρWhere   ρ is average density.That makes :  g  =      4    3    G  π  ρ  rSo in this case ( doubling the radius and filling the space ), the gravitational acceleration at the new radius would be twice as large - a completely different result from the first interpretation of your question.So, as always in physics, you need to be very precise in describing what you mean.

Acceleration due to gravity Does acceleration due to gravity increase when an object at a said rad

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