Q:

What's the thrust to weight ratio of Falcon 9 at landing?

I would like to know what is the envelope of thrust to weight ratios that is available to the Falcon 9 first stage during landing. In other words, what's specifically the lower (and hopefully, if you know, the upper) bound on the thrust to weight ratio?

A:

From Wikipedia, we gain the following value at launch (Pounds deliberately chosen because both are units of force, instead of kg, which is a unit of mass)

1,530,000 lbf thrust
1,194,000 lb weight

Thus, the TWR at launch is 1.28. The maximum is 5, because Falcon 9 will start shutting engines down if the TWR is ever over 5. This is what it is during the flight portion of the launch. Okay, so what would it be during landing? Well, the highest it could be is if the fuel is completely spent, and it is only using a single engine. SpaceX doesn't actually release that, but it is estimated to be between 23- 26 metric tons. Okay, so what does that entail? Well, with only 1 engine, it is thrusting 1/9th of the maximum thrust. There is some information that the engine can throttle down as well, by 40%. Most likely this means 40% lower, per Space Shuttle performance, but it could eb interpreted in other ways. The weight is between 50-57 thousand pounds. So, what is that TWR? About 1.8-2.05. The first stage is usually returned almost empty, so this is probably a good estimate of the TWR at landing.  Bottom line is, the following values are estimated TWR for the Falcon 9:

Launch- 1.28
Maximum in flight- 5
Landing- 1.8-2.05 (Estimated maximum, actual could be lower if there is remaining fuel)

