astrophotography – How do I eliminate the shake I’m getting using a supertelephoto lens and tripod to shoot the moon?

I agree with @xenoid in that a system that uses Arca-Swiss style dovetail rails (they don’t need to be Arca-Swiss brand name) gives you an advantage because these rails come in various lengths and this lets you move rail forward/aft in the saddle to balance the camera’s center of mass over the tripod to reduce flexure and vibration.

A Benro GH2 is a gimbal head with a 50 lb load capacity… around $350 USD.

But it need not be a gimbal head to work well. Check the load rating for the head you are considering. A Benro B3 or above (e.g. B4, B5) would also be fairly beefy and in the $200-250 USD price range.

Regarding exposure…

Lunar exposures are fairly easy. The base rule is the “Looney 11” rule … at f/11, a good starting point for the shutter speed is the inverse of the ISO. So at ISO 100, that’s 1/100th. At ISO 200 it’s 1/200th. You need not use f/11 … but that’s the f-stop where the shutter speed is the simple inverse of the ISO. Trade f-stops for shutter speed if you prefer to use a different f-stop.

A caveat is to beware atmospheric extinction. This is the notion that while the moon is in sunlight, you are shooting through a lot of atmosphere and it absorbs (extinguishes) some of the light. That’s why it’s Looney 11 instead of Sunny 16 rules. If the moon is very low in the sky (rising or setting) then you’ll have more atmosphere to shoot through, which means more extinction … so you’d need a longer exposure. Also an atmosphere that has more dust, smog, or other particulates will absorb more light and need a longer exposure to compensate.

Here’s a sample image:

Moon exposed using Looney 11 rule

The above was shot at f/11, ISO 100, 1/100th sec.

I used a TeleVue NP101is (4″ apochromatic refractor with an f/5.4 focal ratio and 540mm focal length) combined with a TeleVue 2x PowerMate (an image-space telecentric teleconverter). This gave me an effective focal length of 1080mm at f/10.8 (f/11). The camera was a Canon 60Da (APS-C).