Answer:
the altitude of these satellites above the surface of the earth;
35790 km ( SI units )
22243.63 miles ( U.S. customary unit )
Explanation:
Given the data in the question;
Time taken by the satellite to complete on revolution is 23.934 hours
= 23.934 × 60 × 60 = 86162.4 seconds
now, let h represent altitude, r represent Orbit radius, v represent Orbit speed.
we know that
v² = GM/r
= gR²/r
= (9.81m/s² × ( 6.37 × 10⁶ m)²) / r
v = 19.95 × 10⁶ / √r ---------- let this be equation
also;
time t = 2πr/v
86162.4 s = 2πr/v -------- let this be equation 2
a) Determine the altitude of these satellites above the surface of the earth in both SI and U.S. customary units
we substitute v in equation into equation 2
so
86162.4 s = 2πr / (19.95 × 10⁶ / √r)
r = 42.16 × 10⁶ m
so, altitude h = r - R
h = 42.16 × 10⁶ m - 6.37 × 10⁶ m
h = 35790000 m
convert to kilometer
h = 35790000 / 1000
h = 35790 km
Convert to miles
h = 35790 / 1.609
h = 22243.63 miles
Therefore, the altitude of these satellites above the surface of the earth;
35790 km ( SI units )
22243.63 miles ( U.S. customary unit )
