In 2016, Every country was given their own Earth, presumably by a hyper-advanced alien race. All UN member nations, minus Vatican City but including Taiwan, Kosovo, North Cyprus, Palestine, West Sahara, and South Ossetia, were given Earths occupying the same orbit between Venus and Mars, 1 AU away from the Sun. As anyone familiar with orbital mechanics can tell you, this arrangement, termed a Klemperer Rosette, should be unstable; computer simulations indicate that the orbits should have collapsed after less than five years, but somehow the Earths stay neatly arranged in a circle.
Most countries were able to get their economies more or less working within a decade. Japan, Saudi Arabia, South Korea, and some other unfortunate countries collapsed and reformed due to food shortages, as these countries did not grow enough of their own food. The shock of famine caused birth rates in most of these countries to rebound once stability had been reestablished; for example, Japan has 700 million people, of whom 60 million live on the Home Islands.
Radio contact with other planets turned out to be fairly easy; most planets have several dedicated interplanetary communications stations on mountains and in desert areas, while hobbyists can build their own less-sophisticated arrays at home. Light-speed delay is 31 seconds between adjacent worlds (15.6 seconds each way), so internet isn't really possible, but a networked query-answer system allows for the transfer of messages and information, which is one of the few goods tradable between planets.
The USA was the first country to build a moon base in 2029, three years ahead of the Chinese and their moon ("Two!" some Chinese will argue, since they took place in December and January). Curiously, only the US's moon had the famous flag on it, so the red flag now flies on China's moon, now named Yue. Since then, 39 other nations have built moon bases, the most recent being Singapore. Generally, these bases include electromagnetic mass drivers.
Lunar mass drivers are the primary launch points of spaceships and cargo. High tech items like nanomachines, germline cultures, and true AI are almost the only physical things that are traded between planets, since they cram a lot of value into a small mass. Since mass drivers can also be used as kinetic bombardment weapons, the more advanced nations get suspicious when less advanced countries insist on building mass drivers for "trade." Several planets too underdeveloped to build their own mass drivers have drivers built and operated for them by other countries; the country operating drivers on the most moons is, of course, Bharat.
Human travel between planets is doable but rare. In 2050, the first interplanetary voyage was undertaken as a crew of Chinese astronauts were launched from Yue to the Philippines (as the world was still called, then); this was a one-way mission, but they lived as celebrities on their new world until they were able to be returned in 2083. The USA followed suit with a mission to Peru in 2051, and the Indians thereafter with a mission to Sri Lanka in 2062. 14 others have thus far completed manned missions to other planets, the most recent being Kenya in 2134. In recent years, true spaceships with the ability to travel between Earths' orbits under their own power have become usable to private enterprises, and the first space colonies have gone up starting in the 2090s. The successor to the United Nations, the United Planets, is located on a large space colony orbiting Bharat.
A side-effect of the Earths appearing is the uptick in asteroid impacts. Having 200 times the mass in a single orbit and 200 times the area to for an object to hit adds up to extinction-level events expected to happen once every century or so. So far, there have been two such strikes: One struck Bhutan in 2082 and destroyed much of South America's ecosystems, while the other struck Qatar in 2095 and kicked up a tsunami that wiped out many settlements. Other than that, though, the two planets seem to be doing okay. Potential asteroid impacts are tracked much more closely now; the only upcoming impact expected is one which is believed to be 40% likely to strike Bhutan (again!) in 2235.