What equations should I use to calculate the effective value of g, the acceleration of gravity (in meters/second^2), at 5800 km above the earth's surface?
The effective value of g is inversely proportional to the SQUARE of the distance from the center of the earth.
The radius of the Earth is 6378 km. At 5800 km altitude, you are 12,178 km from the center.
g will lowered by a factor (6378/12178)^2