Space wave propagation is possible for which frequency range?

$A$ carrier signal $C(t)=25 \sin(2.512 \times 10^{10} t)$ is amplitude modulated by a message signal $m(t)=5 \sin(1.57 \times 10^{8} t)$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?

$A$ $TV$ tower has a height of $100 \ m$. The average population density around the tower is $1000 \ \text{per} \ km^2$. The radius of the earth is $6.4 \times 10^6 \ m$. The population covered by the tower is:

The height of a $TV$ transmitter antenna is $100 \ m$. What is the area covered by the transmitter for broadcasting? $(R = 6.4 \times 10^{6} \ m)$

$A$ communications Earth satellite:

For the output of an $AM$ detector circuit to follow the envelope of the carrier wave,which condition must be satisfied? ($T_c$ is the time period of the carrier wave.)