Question

A team of astronomers discovers a planet that has a radius of 2.24 * 10^7 m. Based on the motion of nearby objects, they have estimated that the gravity at the surface of the planet is 4.59 m/s^2. What is the approximate mass of this planet

Answer 1

The approximate mass of the planet is 3.457 × 10²⁵ kg.

Step-by-step explanation:

The mass of a planet can be calculated using the formula for the acceleration due to gravity. The formula for the acceleration due to gravity is given by:

g = G (M/R²)

Where:

• g is the acceleration due to gravity at the surface of the planet
• G is the gravitational constant (approximately 6.67 × 10⁻¹¹) N(m²/kg²))
• M is the mass of the planet
• R is the radius of the planet

Plugging in the values from the given information, we can solve for the mass:

4.59 = 6.67 × 10⁻¹¹ (M/(2.24 × 10⁷)²)

Simplifying the equation:

4.59 = 6.67 × 10⁻¹¹ (M/5.0176 × 10¹⁴)

Multiplying both sides by (5.0176 × 10¹⁴) to isolate the mass:

4.59 × 5.0176 × 10¹⁴ = 6.67 × 10⁻¹¹ M

Simplifying:

2.3059104 × 10¹⁵ = 6.67 × 10⁻¹¹ M

Dividing both sides by (6.67 × 10⁻¹¹) to solve for M:

M ≈ 3.457 × 10²⁵ kg

The approximate mass of the planet is 3.457 × 10²⁵ kg.