How can I use c++ for astrophysics programs? I'am fond of astronomy how can I use c++ to create something usefull for me.

Answer 1

Just a few quick ideas:
Implement some Runge-Kutta methods and use them to find stable orbits for a rocket in the gravity fields of earth and moon.
Write a tool, that handles CCD image preprocessing or one that finds variable stars in a series of images and returns their changes in brightness over time.
Make a tool, that notifies you when the ISS is visible form your location.

Answer 2

Can I create a program that calculate the escape velocity and the force of gravity?

Answer 3

I think you can use the formulas applying them to the objects when needed which you settle using classes