Answer:
26621 km
Step-by-step explanation:
We are given;
Mass: m = 5.98 x 10^(24) kg
Period; T = 43200 s
Formula for The velocity(v) of the satellite is:
v = 2πR/T
Where R is the radius
Formula for centripetal acceleration is;
a_c = v²/R
Thus; a_c = (2πR/T)²/R = 4π²R/T²
Formula for gravitational acceleration is:
a_g = Gm/R²
Where G is gravitational constant = 6.674 × 10^(-11) m³/kg.s²
Now the centripetal acceleration of the satellite is caused by its gravitational acceleration. Thus;
Centripetal acceleration = gravitational acceleration.
Thus;
4π²R/T² = Gm/R²
Making R the subject gives;
R = ∛(GmT²/4π²)
Plugging in the relevant values;
R = ∛((6.674 × 10^(-11) × 5.98 x 10^(24) × 43200²)/(4 × π²))
R = 26.621 × 10^(6) m
Converting to km, we have;
R = 26621 km