Does Earth's Size Affect Your Weight?

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SUMMARY

The discussion centers on the relationship between Earth's size and individual weight, specifically examining how gravitational attraction is influenced by the Earth's radius. According to Newton's Law of Gravity, weight is inversely proportional to the square of the distance from the Earth's center. If Earth were to triple its diameter while maintaining the same mass, an individual's weight would decrease to one-ninth of their current weight. Conversely, if Earth were half its current diameter, weight would increase due to the reduced distance from the center of mass.

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  • Understanding of Newton's Law of Gravity
  • Basic knowledge of gravitational force calculations
  • Familiarity with concepts of mass and radius
  • Knowledge of inverse square relationships in physics
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  • Explore advanced gravitational theories beyond Newtonian physics
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Students of physics, educators teaching gravitational concepts, and anyone interested in the effects of planetary size on weight and gravity.

syano
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Is the strength of gravity dependent on other things besides mass such as volume or density? For instance, if our Earth had three times the diameter as it does now but contained the same amount of matter would I weigh any more or less? Or if our Earth had half the diameter as it does now would I weigh the same?

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Newton's Law of gravity

Yes, gravitational attraction depends on distance. Your weight on the Earth's surface is related to your distance from the Earth's center according to Newton's Law of gravity:
[tex]F = G\frac{Mm}{R^2}[/tex]
where M = mass of Earth, m = mass of you, and R = radius of Earth (treating the Earth as symmetrical ball). G is a constant.

So if you keep the Earth's mass (M) the same, but triple its radius, your weight would be 9 times less.
 

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