You need a coil to radiate the RF signal and it also comes in handy to add a variable capacitor for tuning.
Use pin 2 (trigger) to modulate the signal from the 555 oscillator.
Heres a link to a schematic of a 555 AM tranmitter, about halfway down the page. Replace the first 555 with your audio amp to modulate the carrier.
From looking at the schematic it appears to me that the 555 on the left generates the RF carrier and other 555 is used as a PWM modulator in which the modulating audio signal is entered via pin 5 ( control voltage).
The coil and and variable cap is for tuning the transmitter to a particular RF frequency on your AM radio.
So why wod be the C varible!(anser: To set the transmiting freqency)
Yep looks about right. So like you suggested if you use a coil between the antenna and ground, the transmitter will radiate alot of harmonics and you would pic up the signal at several places along your AM radio dial.
The sim graph doesnt look right. The input signal looks like a 500Hz sawtooth type waveform and the carrier is oscillating 900 Khz and the graph shows the sawtooth signal riding on the higher 900 khz frequency, hows that possible ? The graph looks like an odd form of frequency modulation. For amplitude modulation the audio signal should control the amplitude envalope of the high frequency carrier, the transistor in your circuit appears to be controlling the output power instead.
Heres a suggestion:
Since your using a transistor why not build a simple Harley Oscillator and use the 555 timer to transmit in morse code ?