What is a legitimate government?

a. one in which government leaders obtain and keep powers by using force
b. one that offers the fastest solutions to a nations problems and citizen needs
c. one that is created by a union of many smaller groups that could not obtain power on their own.
d. one that is accepted by their people and other governments as the sovereign authority of a nation

The answer to this question is: One that is accepted by their people and other governments as the sovereign authority of a nation
To be considered as 'legitimate' in a democratic country, the government must be chosen based on how the people want them to be represented by the candidates. After being chosen, the government officials have the obligation to fulfill all the promises that they ,made during the campaign for the people that supported them

The one that most represents the earths mantle would be the skin since the mantle is the upper part of the earths depths which is just like the skin of an apple.