Final answer:
Robert Hutchings Goddard introduced the idea of using solar energy for propulsion through solar sails in his research. This leverages the conservation of momentum, allowing a spacecraft to accelerate using the momentum carried by solar radiation. Option C is correct.
Step-by-step explanation:
The student is asking which idea Robert Hutchings Goddard introduced in his research which is titled "A Method of Reaching Extreme Altitudes." The correct answer is solar energy.
Goddard is well known for his innovative work in rocketry and spaceflight, which culminated with him theorizing the use of solar energy as a means of propulsion for spacecraft through the concept of solar sails. This idea was grounded in the understanding that light carries both energy and momentum that can exert pressure, and hence can be used for propulsion without the need for carrying fuel if a spacecraft is equipped with a large, reflective light sail.
The fundamental physics principle behind the technology of solar sails is the conservation of momentum. This principle underlies the potential for utilising the pressure exerted by solar radiation for propulsion, and thus links directly to Goddard's foresight into possible space travel technologies.