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Halley's comet is a potato-shaped lump about ten miles long with a mass estimated at 10 billion tons, most of which is water ice.

I generally eschew this construction fearing that it is wrong except for some specific cases. I was surprised that the above sentence is grammatically correct.

Shouldn't something like this be more appropriate :

Halley's comet is a potato-shaped lump about ten miles long with a mass estimated to be around 10 billion tons, most of whichD is water ice.

PS: Also can these uses of 'estimated at' be grammatically correct too?

His weight is estimated at 50 kgs OR The elephant's weight is estimated at 500 kgss

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In short, yes, that construction is entirely correct. And yes, both of the sentences that you wrote are correct as well.

This sort of construction can be seen all over the place. The first example that comes to mind is in a boxing ring:

Announcer: And in the blue corner, weighing in at over 200 pounds, we have Rocky the destroyer!

Here are a few more examples from Merriam-Webster:

Examples of estimate:
They estimated the distance at about three miles.
The cost of the project has been estimated at about 10 million dollars.

As long as we follow our rules with prepositions, we should be fine. After "at," we have to have a noun, which we do in this case with "tons."

Google Ngram confirms that both options are almost equally popular:

However, if you did want other options, this works as well:

with an estimated mass of 10 billion tons, most of which is water ice.

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