The acceleration due to gravity, denoted as "g," refers to the acceleration experienced by an object when it is in free fall. On the surface of the Earth, the value of g is approximately 9.8 m/s^2. However, this value can vary at different locations and under different conditions.

1) Acceleration at a depth of 2000 km:

At a depth of 2000 km below the surface of the Earth, the acceleration due to gravity will be different from the value on the surface. To calculate this, we can use the formula for the gravitational field inside a uniform sphere:

g = (G * M) / (r^2)

Where:
- G is the gravitational constant (approximately 6.67 × 10^-11 N m^2/kg^2)
- M is the mass of the Earth
- r is the distance from the center of the Earth

To simplify the calculation, we can assume the Earth to be a sphere of uniform density. The mass (M) can be expressed as the product of density (ρ), volume (V), and gravitational acceleration at the surface (g):

M = ρ * V = ρ * (4/3 * π * R^3)

Where:
- ρ is the density of the Earth
- V is the volume of the Earth
- R is the radius of the Earth

Substituting the expression for M into the formula for g, we get:

g = (G * ρ * (4/3 * π * R^3)) / (r^2)

At a depth of 2000 km, the distance from the center of the Earth (r) will be the radius of the Earth (R) plus the depth (2000 km):

r = R + 2000 km

Substituting this value into the equation, we can calculate the acceleration due to gravity at this depth.

2) Acceleration at a height of 500 km:

Similarly, at a height of 500 km above the surface of the Earth, the acceleration due to gravity will also be different. In this case, the distance from the center of the Earth (r) will be the radius of the Earth (R) minus the height (500 km):

r = R - 500 km

Using the same formula as above, we can calculate the acceleration due to gravity at this height.

It is important to note that these calculations assume a simplified model of the Earth and do not take into account variations in density or the presence of other celestial bodies. In reality, the acceleration due to gravity can vary slightly based on location and other factors.