Final answer:
To find the mass of Planet Z, we can use the formula for gravitational acceleration and solve for the mass. Plugging in the given values for gravity, radius, and the universal gravitational constant, we find that the mass of Planet Z is approximately 1.14 × 10²⁴ kg.
Step-by-step explanation:
To find the mass of Planet Z, we can use the formula for gravitational acceleration:
g = (G * M) / r²
Where g is the acceleration due to gravity, G is the universal gravitational constant, M is the mass of the planet, and r is the radius of the planet.
Given that the diameter of Planet Z is 1.8 × 10⁷ m, we can calculate the radius by dividing the diameter by 2:
r = 1.8 × 10⁷ m / 2 = 9 × 10⁶ m
Plugging in the values of g = 19.5 m/s², G = 6.674 × 10⁻¹¹ N⋅m²/kg², and r = 9 × 10⁶ m into the formula, we can solve for M:
19.5 m/s² = (6.674 × 10⁻¹¹ N⋅m²/kg² * M) / (9 × 10⁶ m)²
Simplifying the equation:
M = (19.5 m/s² * (9 × 10⁶ m)²) / (6.674 × 10⁻¹¹ N⋅m²/kg²)
Calculating this:
M ≈ 1.14 × 10²⁴ kg
Therefore, the mass of Planet Z is approximately 1.14 × 10²⁴ kg.