How Does Distance Affect Gravitational Force?

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SUMMARY

The gravitational force experienced by an object decreases with the square of the distance from the center of the Earth. If an apple weighs 1 N at the Earth's surface, its weight at a distance three times further from the center of the Earth can be calculated using the formula f = m1m2/d². By substituting the distance into the equation, the weight at three times the distance is determined to be 1/9 N, not 1/3 N. This conclusion emphasizes the importance of correctly applying gravitational equations and understanding the inverse square law.

PREREQUISITES
  • Understanding of gravitational force and the inverse square law
  • Familiarity with the formula f = m1m2/d²
  • Basic algebra for manipulating equations
  • Knowledge of the concept of distance in gravitational contexts
NEXT STEPS
  • Study the derivation of the gravitational force formula f = G(m1m2)/d²
  • Explore the implications of the inverse square law in physics
  • Learn about gravitational fields and potential energy
  • Investigate real-world applications of gravitational force calculations
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Students studying physics, educators teaching gravitational concepts, and anyone interested in understanding the mathematical relationships governing gravitational forces.

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Homework Statement


If an apple at the surface of the Earth has a weight of 1 N, its weight three times as far away from the centre of the Earth is


Homework Equations



f = m1m2/d^2

The Attempt at a Solution



1N/3times

so is it 1/3?
or since it's three times

1/9?
 
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Physix1233 said:

Homework Statement


If an apple at the surface of the Earth has a weight of 1 N, its weight three times as far away from the centre of the Earth is


Homework Equations



f = m1m2/d^2

The Attempt at a Solution



1N/3times

so is it 1/3?
or since it's three times

1/9?

Welcome to the PF. I'd suggest that you be a little more careful and rigerous in writing the equations.

On your first equation, you are missing a constant, right? It may not be important in the calculation you are doing, but gravitational force is not equal to what you wrote as m1m2/d^2. It is proportional to that, but not equal.

And put some variables into the equation to get the ratio, don't just guess. Call the radius of the Earth R, and write the two force equations for the two spots. Then divide them -- what do you get?
 

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