I need to know why an FM broadcast can't travel too far (from one side of the earth to other) like an AM broadcast that could travel thousands of miles after getting reflected from the ionosphere.
Why can't FM signals be sent to the ionosphere for high range broadcast?
It's not FM modulation versus AM modulation. It's the frequencies used.
The ionosphere is what controls this.
AM Broadcast radio frequencies are from 540KHz to 1700KHz. Those frequencies are low enough that they will bounce off the ionosphere and travel long distances. At night, the layer of the ionosphere that reflects the signal is much higher in the sky, so it bounces farther. During the day, the suns energy charges the layer of the ionosphere much closer to the surface of the earth, so they signals bounce off a layer much closer and don't travel as far.
FM Broadcast uses frequencies 87.8MHz to 108MHz. Those frequencies are high enough that they pass through that charged level of the ionosphere rather than bouncing off it most of the time.
RF power level doesn't play into it usually. A 1000 watt AM broadcast station can still travel thousands of miles, where a 100,000 watt FM broadcast station usually cannot.
However….
Sometimes the atmosphere will do a thing called ducting, where the signals can get trapped between two layers and FM Broadcast, as well as TV and other bands, can bounce along in that duct and travel long distances. Some hobbyists like to "DX" FM broadcast and TV signals from across the Atlantic ocean. It can be a very rare occurrence and short lived, but it does happen.
If you want to learn more, do some googling on "Maximum Useable Frequency" and "Propagation Ducting".