You could make the moon move relative to the camera.
Select the camera and ⇧ ShiftS snap the cursor to it. Then add an empty at that position. ⇧ ShiftA
Select the moon. ⇧ Shift select the the empty and parent the moon to the empty ⎈ CtrlP.
Select the empty. Add a Copy Location Constraint. Choose the camera as the target.
Bottom right of your second screenshot, uncheck the sequencer.
The sequencer tells is essentially part of Blender's integrated video editor.
Checking Use Sequencer tells Blender to render the contents of the Video Editor rather rendering the scene.
You can clearly see the tracker shifting on the video posted on the question, and it happens at the moment where the reconstruction fails.
Successful reconstruction can only be achieved with accurate tracking
You should aim to have a solve error of less than 0.3 pixels.
There are plenty of tools to help you get more accurate tracking.
Solve error ...
Select the camera object in the object list in the top right corner. Then press the forward slash key "/" to isolate the camera. This will hide everything but the camera and zoom in/center the viewport onto the camera.
From there, I'm sure you can figure out how to rescale and reposition the camera to fit the scene.
Changing the units and unit scale should ...
You can link the camera to the viewport and then rotate/pan/zoom as you are used to from the viewport - very handy!
press N tp show right menu
view lock accordeon
check "lock camera to view"
All credits to this guy on YouTube...