Finding the spring compression length for an object to reach $U = 0$

I have a question on the following, pertaining to only parts c and d (b was shown to provide the mass of the asteroid and radius):

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I’m going to define the mass of the asteroid here as $M_A$ and the radius of the asteroid here as $R_A$.

My thought process is as follows:

• The object underwent work to go from radius $R_A$ to radius $r$ (where $U(r) = 0$)
• The object’s energy at the initial state is its gravitational potential energy at $R_A$ and the energy of the spring. $E_i = -frac{GMm}{R_A} + frac{1}{2}kx^2$ thusly
• The object no longer has any potential energy at its final state, so all of its energy must be kinetic, equal to $frac{1}{2}mv^2 = E_f$
• The energies are likely equal to eachother ($E_i = E_f$) since the energy of the system should be conserved?… It underwent work, but that was due to the extra stored potential by the spring?.. perhaps that’s not true.

Which of my assumptions are wrong, and how can I go about tackling this logically? Note, this isn’t homework but an example to enforce my learning. Thanks!