How to prove the equality of inertial and gravitational masses on the basis of astronomical observations?

If the inertial and gravitational masses are equal, the acceleration of gravity does not depend on the mass of the attracted body. The acceleration of a freely falling stone and the centripetal acceleration of the Moon do not depend on their masses, but are determined only by the distance of these bodies from the center of the Earth.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.