In 2005 the world's economic system is preeminently dominated by the United States, with a GDP of $11.7 trillion. The other trillionaire countries in existence today are Japan ($4.4 trillion), Germany ($2.0 trillion), China ($1.7 trillion), Britain ($1.7 trillion), France ($1.5 trillion) and Italy ($1.2 trillion). So, let's us assume that on the basis of economic size alone, those countries would constitute G7 (sorry Russia and Canada).
Within five years, China overtakes Germany, to become the third largest economy behind the United States and Japan. This is in spite of China's growth beginning to slow from the breakneck double digit rates of the 1990s to around 7% in 2010, and later to around 5% at the end of the following decade. China's economy slowly cools, but Japan's economy is stone cold in comparison, with a real growth rate of barely a percentage point per year in the coming decade. In 2016, China passes the $5 trillion barrier and overtakes Japan to become number two in the world.
By the middle of the century, the G7 summit would more likely to be held in Recife than Rambouillet. The countries which ran the world at the beginning of the year would be fewer in number, and those which still survive at the top will necessarily have required considerable economic and social transformation. Ruling the roost would be China with a GDP of $44.5 trillion. The United States was overtaken nine years earlier in 2041, and has clearly lost dominance with a comparatively modest GDP of $35.2 trillion. Indeed India, with the most favourable demographic profile of the major powers, is closing in with a GDP of $27 trillion. Far behind the big three are Japan ($6.7 trillion), Brazil ($6.1 trillion) and Russia ($5.9 trillion). Britain remains having a voice in the world through its Athenian power play and stays in G7 as the sole European power, with a GDP of $3.8 trillion.