The acceleration due to the Earth's gravity at any height \(h\) above the surface of the Earth is given by the equation $$ g=-G \frac{M}{(R+h)^{2}} $$ where \(G\) is the gravitational constant \(\left(6.672 \times 10^{-11} \mathrm{~N} \mathrm{~m}^{2} / \mathrm{kg}^{2}\right), M\) is the mass of the Earth \(\left(5.98 \times 10^{24} \mathrm{~kg}\right), R\) is the mean radius of the Earth \((6371 \mathrm{~km})\), and \(h\) is the height above the Earth's surface. If \(M\) is measured in \(\mathrm{kg}\) and \(R\) and \(h\) in meters, then the resulting acceleration will be in units of meters per second squared. Write a program to calculate the acceleration due to the Earth's gravity in \(500-\mathrm{km}\) increments at heights from \(0 \mathrm{~km}\) to \(40,000 \mathrm{~km}\) above the surface of the Earth. Print out the results in a table of height versus acceleration with appropriate labels, including the units of the output values. Plot the data as well.

To solve this task, you can follow these steps: 1. Define the given constants: gravitational constant \(G = 6.672 \times 10^{-11} \mathrm{N} \mathrm{m}^{2} / \mathrm{kg}^{2}\), mass of Earth \(M = 5.98 \times 10^{24} \mathrm{kg}\), and the mean radius of Earth \(R = 6371 \times 10^3 \mathrm{m}\). 2. Construct a loop to cycle through heights from 0 to 40,000 km in 500 km increments, be sure to convert these increments to meters. 3. Within this loop, calculate the acceleration due to Earth's gravity (g) for each height \(h\) using the formula \( g=-G \frac{M}{(R+h)^{2}}\). 4. Print each corresponding height and its calculated acceleration in a table, ensuring that the units are correctly labeled. 5. Finally, plot the data by placing the heights on the x-axis and the corresponding accelerations on the y-axis, and label the axes appropriately. You can implement this code in any programming language. After the code is implemented, it is important to validate its accuracy with multiple test cases.