furthermore, the fascination with space missions generates hordes of inspired children who will study and thus this plant the seeds of scientists for future generations who will solve tomorrow's problems (in practice, it is a long-term investment)
of the race to the moon we now have the practical and common use of transistors and chips, led, batteries, pace makers, medical pumps, thermal insulation and dozens of other things we use and take for granted every day
to prefer little and bad immediately at the expense of much and good in the future is a very short-sighted and stupid attitude
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Imagine one day the first Dalit in space, what message it would send.
You can think of these as lower levels of the pyramid that support the rocket at the top. Each of these require people to learn these things at a very high level. Local firms must learn to manufacture complex components at high tolerances, universities must produce graduates who are good enough to tackle these problems, government departments have to build the expertise to manage these projects. Forming even more of a broad base of the pyramid.
Once you have built the rocket, all this expertise doesn't just go away. All these trained people, and the processes and institutions that created those trained people, will not go away. They will go into other areas and solve other problems in a much better fashion than if they had not been trained such.
If you instead try to build a car instead, the pyramid will be much shorter, and the type of expertise required will be much less. The training processes will be worse. The spillover effects into the economy would be much less.