Final answer:
The gravitational constant, denoted as G, can be checked by substituting Earth's known mass and radius into the formula for the acceleration due to gravity at Earth's surface. The accepted value of G is approximately 6.67×10⁻¹¹ N·m²/kg².
Step-by-step explanation:
To check the value of the gravitational constant using the mass and radius of Earth, we can look at the formula for the acceleration due to gravity (g) at the Earth's surface, given by the formula:
g = (G × M) / R²
Where:
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- G is the gravitational constant
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- M is the mass of Earth
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- R is the radius of Earth
We know that the average acceleration due to gravity (g) on Earth's surface is approximately 9.81 m/s². Substituting the known values and solving for G should yield:
G = g × R² / M
G = (9.81 m/s²) × (6.371×10¶ m)² / (5.971×10²⁴ kg)
Upon calculation, we expect to find G to be approximately 6.67×10⁻¹¹ N·m²/kg², which corresponds to the value provided in the given data and is consistent with the currently accepted value of the gravitational constant.