Question

Earth is not a perfect sphere. Its radius as well as the value of g vary with latitude. (a) Calculate Earth’s mass given the acceleration due to gravity at the North Pole is 9.807 m/s2 and the radius of the Earth at the pole is 6356.8 km.Calculate Earth’s mass given the acceleration due to gravity at the North Pole is 9.807 , {m/s}² and the radius of the Earth at the pole is 6356.8 km.

a) 4.54 × 10²⁴ kg
b) 5.98 × 10²⁴ kg
c) 6.81 × 10²⁴ kg
d) 7.46 × 10²⁴ kg

Answer 1

Earth's mass can be calculated using the acceleration due to gravity at the North Pole and the radius of Earth using Newton's Universal Law of Gravitation. The mass of the Earth comes out to be approximately 5.98 × 10²⁴ kg when proper substitutions are made in the formula.

Step-by-step explanation:

To calculate Earth's mass given the acceleration due to gravity (g) at the North Pole, we can use Newton's Universal Law of Gravitation.

The formula is g = G * M / R², where G is the gravitational constant (6.67430 × 10⁻¹¹ N·m²/kg²), M is the mass of the Earth, and R is the radius of the Earth at the North pole.

Given that g is 9.807 m/s² and R is 6356.8 km, we can rearrange the equation to solve for M as such:

M = g * R² / G

Converting R to meters gives us 6356800 meters.

Using these values, the calculation yields M = (9.807 × (6356800)²) / (6.67430 × 10⁻¹¹), which results in a mass of approximately 5.98 × 10²⁴ kg.

Therefore, the correct answer to the question is b) 5.98 × 10²⁴ kg, which matches the accepted value of Earth's mass.