Several sources lately incline me to think of world (or solar) government as very likely in the long run. First, I read Betrand Russell, in a 1950 essay The Future of Mankind, advocating violence to make a world government:
Before the end of the present century, unless something quite unforeseeable occurs, one of three possibilities will have been realized. These three are:
I. The end of human life, perhaps of all life on our planet.
II. A reversion to barbarism after a catastrophic diminution of the population of the globe.
III. A unification of the world under a single government, possessing a monopoly of all the major weapons of war. …
A world government is desirable. More than half of the Amerian nation, according to a Gallup poll, hold this opinion. But most of its advocates think of it as something to be established by friendly negotiation, and shrink from any suggestion of the use of force. In this I think they are mistaken. I am sure that force, or the threat of force, will be necessary. …
The governments of the English-speaking nations should then offer to all other nations the option of entering into a firm alliance, involving a pooling of military resources and mutual defense against aggression. In the case of hesitant nations, … great inducements, economic and military, should be held out to produce their cooperation. … When the Alliance had acquired sufficient strength, any Great Power still refusing to join should be threatened with outlawry, and, if recalcitrant, should be regarded as a public enemy. The resulting war … (more)
Russell was right that Americans then favored a world government:
In March 1951, nearly half (49%) of Americans thought the United Nations should be strengthened to make it a world government with power to control the armed forces of all nations, including the United States, while 36% thought it should not. (more)
Seems they still favored it in 1993:
In a  telephonic survey financed by the WFA, 58% of 1200 adult American citizens polled thought that to have practical law enforcement at home and abroad, a limited, democratic world government would be essential or helpful (with 35%) disagreeing). For effective enforcement of laws, 66% of those questioned felt there should be a world constitution, more than double the number who disagreed. … 82% of respondents felt the UN Charter should be amended to allow the UN to arrest individuals who commit serious international crimes, and 83% felt that leaders making war on groups within their country should be tried by an International Criminal Court. (more)
In 2007, much of the world also agreed:
A total of 21,890 people were interviewed between July 2006 and March 2007 [in 19 nations: US, Mexico, Argentina, Peru, Armenia, Ukraine, Russia, Poland, France, Pales. Terr., Israel, Australia, S. Korea, Thailand, China, Indonesia, India, Philippines, Iran.] …
■ Large majorities approve of strengthening the United Nations by giving it the power to have its own standing peacekeeping force, regulate the international arms trade and investigate human rights abuses.
■ Most publics believe the UN Security Council should have the right to authorize military force to address a range of problems, including aggression, terrorism, and genocide. (more)
Finally, the history of China suggests that, once started, “world” government becomes hard to stop:
This study explores the ways in which the Chinese imperial system attained its unparalleled endurance. … I do not pretend to provide a comprehensive answer. … Rather, I shall focus on a single variable, which distinguishes Chinese imperial experience from that of other comparable polities elsewhere, namely, the empire’s exceptional ideological prowess. As I hope to demonstrate, the Chinese empire was an extraordinarily powerful ideological construct, the appeal of which to a variety of political actors enabled its survival even during periods of severe military, economic, and administrative malfunctioning. …
Centuries of internal turmoil that preceded the imperial unification of 221 BCE … were also the most vibrant period in China’s intellectual history. Bewildered by the exacerbating crisis, thinkers of that age sought ways to restore peace and stability. Their practical recommendations varied tremendously; but amid this immense variety there were some points of consensus. Most importantly, thinkers of distinct ideological inclinations unanimously accepted political unification of the entire known civilized world—“All-under-Heaven”—as the only feasible means to put an end to perennial war; and they also agreed that the entire subcelestial realm should be governed by a single omnipotent monarch. These premises of unity and monarchism became the ideological foundation of the future empire, and they were not questioned for millennia. (more)
Even if a world (or solar) government is inevitable, it is still probably best to not start it too early, before we are able to coordinate sufficiently well.