If Earth were to shrink without a change in its mass, what effect would this have on your weight at the surface?

When considering the effects of Earth's size changing while keeping its mass constant, it is essential to recall the relationship between gravity, mass, and distance. Your weight is determined by the gravitational force acting on you, which is influenced by the mass of the Earth and your distance from its center. The gravitational force can be described by the formula:

[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} ]

where ( F ) is the gravitational force (your weight), ( G ) is the gravitational constant, ( m_1 ) is the mass of the Earth, ( m_2 ) is your mass, and ( r ) is the distance between the center of the Earth and your position.

If the Earth shrinks but its mass remains unchanged, the radius ( r ) decreases. Since the gravitational force is inversely proportional to the square of the distance ( r ), if you reduce ( r ), the gravitational force (your weight) will increase. A smaller radius means you are closer to the center of the Earth, resulting in a stronger gravitational pull acting on you. Thus, under these circumstances, your weight would indeed increase as a consequence of the