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I've heard of "interferometric synthetic aperture radar" being used for Earth observation from satellites and airplanes. Is active radar used interferometrically for astronomical purposes too? Such as characterizing asteroids or space debris, or identifying volatiles in the polar craters of Mercury.

Unfortunately for this idea, Arecibo and FASTare located 173 longitudinal degrees apart and have limited fields of view, so they can't observe the same object simultaneously.

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    $\begingroup$ It's done from satellites in astronomy too, such as ssed.gsfc.nasa.gov/IPM/IPM2012/PDF/Revised_Orals/…, but there may be significant power limitations for trying this from the ground. Astronomical targets are pretty far away! Lunar ranging is done with lasers, which are easier to get a powerful beam. $\endgroup$
    – Ken G
    Commented Sep 25, 2016 at 16:13

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Is radar interferometry used, or feasible, for ground based astronomy?

Yes it is!

My answer to How can we install a radar on radio telescopes like FAST or GMRT? beings:;;

The article is quite informative. It is a summary of "a paper published in the journal Scientia Sinica Information" which appears to be Discussion on the requirements and feasibility of constructing China's near-Earth asteroids radar system. While it is written in Chinese the tables and figures alone are very informative.

They are going for a "planetary scale" or very long range system; out to 0.1 AU or 15 million km for an asteroid is ambitious, and what's really interesting it sounds like their transmitted radar beam will com from "four or five 35-metre (115-foot) diameter radio dishes" rather than one big one.

I've pasted some bits into google translate so far and it looks like they will try to have the option to use the multiple transmitting dishes coherently

(3) X 和 Ka 频段上行天线组阵技术. 在国家高技术发展计划支持下, 我国在上行天线组阵技术研 究方面也已经取得了突破, 成功实现了对地球同步静止轨道通信卫星在 C 频段 (发射频率 6 GHz) 的 3 个天线上行组阵技术验证, 达到了 80% 的合成效率. 后续需要针对频率更高的 X 和 Ka 频段上行天 线组阵, 重点开展上行链路相位延迟变化准确估计技术、时延和相位对齐的精确控制技术和大回路系 统标校技术等研究.

  1. X and Ka band uplink antenna array technology. With the support of the national high-tech development plan, China has also made breakthroughs in the research of uplink antenna array technology, and successfully achieved the C-band communication satellites in geosynchronous geostationary orbit. (Transmit frequency 6 GHz) 3 antenna uplink array technology verification, achieved 80% synthesis efficiency. The follow-up need for higher frequency X and Ka band uplink antenna array, focus on accurate estimation of uplink phase delay changes Research on precise control technology of technology, time delay and phase alignment and large loop system calibration technology.

My answer is very long so I won't recopy the whole thing again here, but there are more details available.

As a follow-up I've also asked in Space Exploration SE:

That question highlights the point that a high power/high spatial resolution upwards-pointing radar system will have plenty of space surveillance applications beyond tracking natural near earth objects!

Okay, how about radar astro-metry?

Source: DESCANSO 211 Wideband Very-Long Baseline Interferometry

Figure 1 from DESCANSO 211 Wideband Very-Long Baseline Interferometry

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