Understanding the Gravitational Force of a Hypothetical Planet: Jupiter’s Size with Earth’s Density

Introduction:

Gravity plays a crucial role in shaping the physical characteristics of planets. In the solar system, Jupiter stands out as a gas giant with a significant gravitational force, which is 2.6 times that of Earth despite its immense size. But what if we were to imagine a planet that is as massive as Jupiter but has the density of Earth? Would it have the same gravitational pull? And, more intriguingly, would it have forms of relief and terrain?

Let’s delve into the scientific calculations and theoretical scenarios that offer insights into such a hypothetical planet.

Gravitational Force Calculation

Formula: Fg GMM/r2

G: Gravitational constant, G 6.673 × 10-11 Nm2/kg2 M1: Mass of the planet M2: Mass of the object being influenced (assuming Earth, M2 5.972 × 1024 kg) R: Radius of the planet

Jupiter’s mass is approximately 1.898 × 1027 kg, and its radius is about 69,911 km. If this planet had the density of Earth (5,514 kg/m3), its mass would be around 5.972 × 1024 kg, similar to Earth’s. However, for it to be as massive as Jupiter, its mass would be 318 times that of Earth’s, or 1.898 × 1029 kg.

Given the formula and these measurements, we can calculate the gravitational force:

Fg (6.673 × 10-11) × (1.898 × 1029) × 5.972 × 1024 / (69,911 × 103)2

After simplifying, we get:

Fg ≈ 9.8 × 2.6 25.48 N/kg

This means the gravitational force would be 2.6 times that of Earth, yielding a surface gravity of approximately 25.48 m/s2, significantly higher than Earth’s 9.8 m/s2.

Planetary Density and Composition

Jupiter, being a gas giant, has a much lower density than a rocky planet like Earth, with a density of about 1.33 g/cm3 compared to Earth’s 5.514 g/cm3. If we were to replace the gaseous material with the equivalent mass in rocks or other dense materials, the planet’s density would increase significantly.

For a planet the size of Jupiter but with the density of Earth, the mass would be so high that it would not just contain a small solid core; it would need to be entirely rocky or metallic to achieve the same density. However, current scientific models suggest that such a configuration is not feasible for a planet of Jupiter's size due to gravitational forces and the compression of materials at such extreme pressures.

Terrain Diversity on a Terran-Jovian Hybrid

Given the immensely high gravitational force and the mass of the planet, the terrain would likely be vastly different from that of Earth. The surface gravity would support much higher mountains, deeper valleys, and more dramatic landscape features. The extreme conditions on the surface might even include liquid metallic hydrogen due to the immense pressure beneath the surface.

However, the analogy to Earth’s terrain is particularly intriguing. If this planet had the same chemical diversity as Earth, it could potentially support diverse ecosystems, ranging from vast deserts and oceans to dense forests and high mountain ranges. The pressure and temperature variations would create unique climatic zones, much like those found on Earth.

Exceptional Planets: TOI-849b

One counterexample to the standard scenario is the exoplanet TOI-849b, which is 40 times more massive than Earth but has had its gaseous atmosphere blown away by its parent star. This makes it the largest known rocky world in the universe. Although its density is higher than a typical gas giant, it is still much lower than that of Earth when considering its mass. If we were to hypothetically adjust the composition of a smaller, more massive planet, the results would be dramatically different.

While Jupiter’s configuration is constrained by its location in the solar system, a hypothetical planet with Earth’s density but Jupiter’s mass would require an entirely new set of physics to explain its existence and characteristics.

Conclusion

Exploring a hypothetical planet that is the size of Jupiter but has the density of Earth raises many interesting questions about planetary formation, density, and surface conditions. While the gravitational force and terrain would inevitably differ from our familiar Earth, the theoretical possibilities offer a fascinating glimpse into the vast and complex universe we inhabit.

In the realm of speculative science, such scenarios help us understand the limitations and possibilities of planetary formation and the diverse environments that could exist across the cosmos.