Abstract

When an object's size diminishes, the physical properties of that object significantly change. This article explores what happens to a planet's gravitational pull, angular momentum, and rotational duration if its radius is halved while maintaining the same mass. By examining these changes, we can understand the profound impact on the environment and astrophysical behaviors.

Introduction

The gravitational force, as derived from Newton's law of universal gravitation, is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers. If the Earth's radius is reduced to half, with the mass remaining constant, the gravitational pull would become much stronger, leading to significant alterations in the environment.

Gravitational Pull and Living Organisms

When the Earth's radius is reduced to half and its mass remains constant, the gravitational pull would increase considerably. This enhanced gravitational force would make it challenging for living organisms to thrive at the surface. The stronger gravitational field would exert a greater pressure on the planet's surface, making it difficult for life to exist in the form we know.

Angular Momentum and Daylight

Another significant aspect to consider is the conservation of angular momentum. The Earth's current angular momentum is a result of its moment of inertia and angular velocity. At its current radius, the Earth's angular velocity is such that a day lasts 24 hours. If the radius is halved, the moment of inertia decreases, necessitating an increase in angular velocity to conserve the total angular momentum.

Using Kepler's third law, we can calculate the new duration of the day. Assuming the current radius of the Earth, which is approximately 6,371 kilometers, and assuming its current period to be 365 days for one revolution around the Sun (a year), the new time period would be:

Let r1 and T1 be the present radius and time period of the Earth, respectively.r2  r1/2Using Kepler's third law: T1/T2^2  r1/r2^3T1/T2^2  2r2/r2^3  2^3/2  8/2  4Since T1  365 days, we get:T2  365 / sqrt(4)  365 / 2  182.5 days

Therefore, if the Earth's radius is halved, the rotational period would be approximately 182.5 days, making days considerably shorter and significantly altering the planet's climate dynamics.

Heat Dynamics and Internal Volcanic Activity

Shrinking the Earth to half its current radius would immediately increase its density. The increased density would result in higher pressure within the Earth's core, which could lead to increased volcanic activity. The core, unable to dissipate its heat efficiently, would cause an elevation in internal temperatures, potentially triggering widespread volcanic eruptions.

Conclusion

Halving the Earth's radius while maintaining the same mass would result in a multitude of drastic changes, including a significant enhancement in gravitational pull, a substantial alteration in the rotational period, and an increase in internal heat that may lead to heightened volcanic activity.