You'll probably never get both acceptably sharp in the same exposure.

What we call Depth of Field (DoF) is just an illusion, although it is usually a very convincing one. But it breaks down with certain subjects. Astrophotography is one subject where we can tell the background is not as sharp as we expect when using DoF formulas and calculating the hyperfocal distance.

There's only one distance from the camera that is in sharpest focus. Everything in front of and behind that field of focus is blurred to one degree or another. DoF is what we call the range in front of and behind the field of focus that appears sharp enough to fool our eyes and brains into seeing things as sharp.

You're fighting several technical limitations with the image you are tyring to take that are very difficult to overcome.

• One is that the moon is 250,000 miles away, give or take a few thousand. Your tree is much closer. While in theory it might be possible to place both within the near and far limits of the DoF, neither will be as sharp as you probably want them to be.
• To get a very near hyperfocal distance you must use a very narrow aperture. This leads to diffraction, which causes everything, even the point of sharpest focus, to degrade due to the higher percentage of light rays reaching the sensor that are being scattered by the edges of the aperture diaphragm. For most FF cameras, anything narrower than about f/10 or f/11 starts to show the effects of diffraction. The smaller the sensor and the pixels on it, the lower the aperture at which diffractions begins to affect the image. This is called the diffraction limited aperture (DLA).
• The other disadvantage of using a very narrow aperture is the resulting increase in exposure time needed. Even if your camera is solidly mounted on a tripod or other stable platform and not moving at all, the moon is moving across the sky at a rate of its own diameter every two minutes. The tree is probably not totally stationary either. Any wind will cause motion in the leaves and branches.
• The moon is lit by direct sunlight. It is very bright. Unless it is very low on the horizon the illuminated parts of the moon are properly exposed at about EV 12 (e.g ISO 200, f/8 , 1/125) or even a bit higher. Your tree is probably nowhere near as bright if it is nighttime. Unless you only want a silhouette of the tree you're probably going to need an exposure values about 15 stops slower at EV -3 (e.g. ISO 200, f/8, 256 seconds) OR put some light on the tree from an artificial light source. Even if you could get both the moon and the tree in proper focus the moon would be totally blown out if the tree were exposed to reveal any degree of detail.

There are a couple of strategies you can use to overcome these obstacles:

• Shoot at a time when the moon is in the sky during early morning or late afternoon. By exposing for the moon the sky and landscape will appear darker than they actually appear to your eyes.
• Composite separate images of the moon and the tree. You'll need to take the exposure of the tree when the moon is not in the field of view.