Answer:
As the mass is not written well, i will use the equation in terms of the gravitational acceleration:
The equation for the period of a satellite is:
[tex]T = 2*pi*\sqrt{\frac{r^3}{g*R^2} }[/tex]
We want to find r, so isolating r we get:
[tex]r = \sqrt[3]{x (\frac{T}{2*pi} )^2*g*R^2}[/tex]
Where:
T = period.
r = radius of the satellite.
R = radius of the planet.
g = gravitational acceleration of the planet.
pi = 3.14159...
g = 78999.64 mi/h^2 (value of a table)
T = 42.391 h.
R = 3958.8 miles
We can replace those values in the equation and get:
[tex]r = \sqrt[3]{ (\frac{42.391}{2*3.14159} )^2*78999.64*(3958.8)^2} = 38,339.5 mi[/tex]
Now this value is measured from the center of the Earth, then the altitude of the satellite measured from the surface of the Earth will be:
H = r - R = 38,339.1mi - 3958.8mi = 34,380.3 mi
