Final answer:
The biggest space mission of the twenty-first century may revolve around Mars or lunar colonization. Enormous challenges include long travel times, communication delays, and the need for autonomous and reliable technology. Achieving these missions requires advanced life-support systems, energy solutions, and possibly choosing between manned and unmanned exploration.
Step-by-step explanation:
The biggest space mission of the twenty-first century could likely be the exploration and potential colonization of Mars, or the establishment of permanent habitats on the Moon. One of the monumental challenges will be the sheer distance and time it takes to travel to places like Mars, as well as the delay in communication with Earth. Technical advancements needed for a successful mission include the development of reliable life-support systems, sustainable energy sources for long periods, such as advanced solar panels or nuclear reactors, autonomous systems for the maintenance and repair of spacecraft, and powerful communication tools to counter the vast distances.
Space exploration with human beings is contrasted with the use of unmanned space probes. While manned missions come with greater risks and require more resources, they also have the potential for profound exploration achievements. The difficulties of such missions, specifically regarding the long travel times to outer solar system destinations and the need for spacecraft to operate autonomously due to communication delays, are significant. Heaters may also be necessary to maintain operational temperatures for instruments, and self-sufficient power sources will be crucial due to the Sun's reduced energy output at those distances.
Whether humanity has a 'destiny in space' is a matter of debate, but as we face challenges and resource scarcity on Earth, the prioritization of space travel might shift. Regardless, the continuation of exploration, be it through manned or unmanned missions, appears to be an indelible part of our collective ambition and pursuit of knowledge.