The Comparison of Planet Zeta and Earth's Radius

Introduction

Planet Zeta has 2 times the gravitational field strength and the same mass as Earth. In this scenario, we will analyze how the radius of Zeta compares with the radius of Earth.

Answer:

1/ square root of 2

Explanation:

Inverse proportionality of it is equal to the square root of the gravitational field.

Final answer:

The radius of planet Zeta is approximately √2 times the radius of Earth.

Explanation:

The gravitational field strength depends on the mass and radius of a planet. In this case, planet Zeta has 2 times the gravitational field strength and the same mass as Earth. This means that the radius of Zeta must be smaller than the radius of Earth. Let's assume the radius of Earth is represented by RE and the radius of Zeta is represented by RZ.

According to the given information, the mass of Zeta (MZ) is equal to the mass of Earth (ME). The gravitational field strength of Zeta (gZ) is 2 times the gravitational field strength of Earth (gE). Using the formula for gravitational field strength, g = GM / R², we can set up the equation for Zeta as: gZ = (G * MZ) / RZ² and for Earth as: gE = (G * ME) / RE².

Since the mass of Zeta (MZ) is equal to the mass of Earth (ME), we can set up the equation as: gZ = (G * ME) / RZ², where gZ = 2 * gE. Rearranging the equation and substituting values, we get: (G * ME) / RZ² = 2 * [(G * ME) / RE²].

Cross-multiplying and simplifying, we find: RZ² = 2 * RE². Taking the square root of both sides, we get: RZ = √(2 * RE²).

Therefore, the radius of Zeta is approximately √2 times the radius of Earth.