This production possibilities curve shows the trade-off between consumer goods and capital goods. since capital goods are a resource, an increase in the production of capital goods today will increase the economy's production possibilities in the future. Therefore, all other things equal (ceteris paribus), producing at which point today will result in the largest outward shift of the PPC in the future?

The amount that will result in the largest outward shift of the PPC in the future is the amount that produces the largest amount of capital goods, and the least amount of consumer goods.

This is simply because consumer goods represent the use of present resources to produce present goods and services, which ultimately leads to the depletion of those resources, and leaves the PPC unchanged.

Capital goods, as the question says, are different because they represent the use of present resources to produce future goods and services, which means that the more capital goods are produced in the economy, the more the PPC shifts outward in the future.

a. the moon was locked into orbit by the earths gravity as it was passing by and capture hypothesis i think

you would times this by how many days there are in a year 365*400=$146000