He then spent 15 months at Mawson Station, Antarctica with the Australian National Antarctic Research Expeditions (ANARE), for the International Geophysical Year (IGY), 1958, as an auroral/radio physicist.

The work required that he spend most of the winter at a remote, 2-man base, near the world's largest Emperor penguin rookery, near Taylor Glacier.

His next assignment was as a staff physicist at the Massachusetts Institute of Technology, where he worked in electro-optics, inertial systems at the Experimental Astronomy Lab, under the direction of Charles Stark "Doc" Draper, and gravitational theory with Rainer Weiss until the summer of 1967.

Chapman was actively involved in the NASA/DOE SPS Concept Development and Evaluation Program (CDEP) in the late 1970s and early 1980s and has since continued to make contributions to the literature on power from space.

In particular, a position paper by the council was instrumental in convincing Ronald Reagan that it was technically feasible to intercept ballistic missiles in flight.

In 1989, Chapman led a privately funded scientific expedition by sea from Cape Town, South Africa to Enderby Land, Antarctica, to gather information about mineral resources before the Madrid Protocol to the Antarctic Treaty made prospecting illegal on the continent.

The second paper, "Power from Space and the Hydrogen Economy," discussed the implications of the recent discovery of vast deposits of methane hydrates under Arctic permafrost and on continental shelves, which may be sufficient to meet all world energy needs for many thousands of years.

Under a $6 million contract from NASA, t/Space developed a plan and re-usable vehicle to support the International Space Station (ISS) for after the shuttle's retirement in 2011.

In July 2010, Chapman presented slides to the US Air Force on the topic of Tactical and Strategic Implications of Space-Based Solar Power (SBSP).

On 23 April 2008, Chapman authored an op-ed in The Australian newspaper, noting a new ice age will eventually occur, that based on current low solar activity it might even be imminent, and "It is time to put aside the global warming dogma, at least to begin contingency planning about what to do if we are moving into another little ice age, similar to the one that lasted from 1100 to 1850.

[8] When it has stabilized in its helio-centric orbit, the vehicle will be renamed Enterprise Station to signify its contents of the first ever human remains in deep space.