Final answer:
The increase in the gravitational field, Δg, due to a spherical deposit of heavy metals below Earth's surface, can be calculated using the gravitational force formula for a sphere and dividing by the gravitational acceleration on Earth's surface.
Step-by-step explanation:
To calculate the increase in gravitational field, Δg, at the surface directly above the heavy metal deposit, we can use the formula for the gravitational force due to a point mass, which is derived from Newton's law of universal gravitation. However, since the deposit is spherical, we need to use the formula for gravitational force outside a sphere, which simplifies as if the entire mass were concentrated at its center.
The increase in the gravitational field, Δg, can be calculated using the formula Δg = (G ⋅ m) / r², where G is the universal gravitational constant, m is the mass of the deposit, and r is the distance from the deposit to the point where Δg is being measured. The mass of the deposit, m, can be found by multiplying its volume, 4/3πr³, by its density.
Given that the radius of the deposit is 1110 m and its density is 8860 kg/m³, the mass m can be calculated as m = 4/3π⋅(1110 m)³⋅8860 kg/m³. The distance from the center of the deposit to the point directly above it on the surface (r) is the depth of the deposit plus the radius of the Earth, since the deposit is within the Earth's crust.
Once Δg has been calculated, it can be divided by the gravitational acceleration at Earth's surface, g, to get Δg/g. To find the precise value, these calculations require the use of a calculator or computational tool.