Answer: the radius of the satellite's orbit is r = 8.78×10⁷m
Explanation:
given the time period, T= 3days
converting the time in days to seconds is given as;
time, T=(3*24*60*60) sec
T=259200 sec
from the force relation;
mv²/r = Gm×M/r²
v²=G×M/r ---------------(1)
and
V=2pi×r/T
V²=4×pi²×r²/T²
====>
from equation (1)
, we have
4×pi²×r²/T²=G×M/r
this becomes; 4×pi²×r³/T² = G×M
r³ = G×M×T²/(4pi²)
r³ = 6.67×10⁻¹¹×(5.97×10²⁴)×(259200)²/(4pi²)
==> r=8.78×10⁷m
radius of the orbit, r=8.78×10⁷ m
