To talk to anyone much beyond the horizon, you need your signal to be reflected off the ionosphere - to go round to the other side of the world, you need multiple reflections from both the ionosphere and the surface of the earth. It is the effect of solar radiation that makes the ionosphere reflective to radio waves - this is why propagation is so much better at solar maxima than at solar minima. The level of ionization - and hence reflectivity - will also vary throughout the day. In darkness, the level of ionization will fall and the ionosphere will become less reflective - but this is also frequency dependent. The propagation forecasts are based on the predicted values of several metrics of which the most relevant to us is usually the MUF - Maximum Usable Frequency. The MUF is related to the propagation path - the figure for you to Europe will not be the same as it is to South America - and it increases during the day as solar radiation ionizes the atmosphere above you and falls over night as the ionization level decays away. I've just run the prediction between my QTH near London and a point somewhere round the west coast of the USA and the figure ranges from something like 7MHz at 6am this morning and 16MHz at 3:30pm this afternoon.
Martin (G8FXC)