How could the fireships in RotS know that Grievous' flagship was crewed by friendlies?

Question

In Revenge of the Sith, Anakin and Obi-Wan land on general Grievous' flagship and after some time find themselves at the controls of it with all the bad guys having abandoned ship. They decide to attempt to land on Coruscant and, when approaching the runway, are not only not fired at but even met by fireships that escort them and put out some fires raging on their ship.

How could the fireships, or anyone on the ground for that matter, have known that Grievous' flagship was crewed or at least steered by friendlies? We even see one of the fireship pilots radioing "We'll take you in.", implying he knows who he's talking to. According to this it was not the initial plan to take over the flagship so they could not have been informed in advance.

Is it just implied that maybe R2 made an emergency call?

EDIT:

The answer to this question further extends on the topic.

Answer 1

Interestingly, there's a slight discrepancy between the Official Junior Novel and Official Film Novelisation. In the former, it's Anakin who contacts the Clone troops flying alongside. In the latter, it's Kenobi and only after the ship is targeted (and shot at) by Republic fighters:

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From the film's Junior Novelisation:

Distantly, he was aware of Obi-Wan and Palpatine following his instructions, of R2-D2 taking up a position at the auxiliary controls, but his fingers were already busy with the unfamiliar controls. First, stop the shooting. This switch? No … There. Quickly, he tapped out a message to the Republic’s clone fighters: General Kenobi and I have taken the ship. The Chancellor is safe. Stop firing. He signed it with his name and the code that would mark it as an authentic message, and sent it off.

and the film's Official Novelisation

The cruiser bounced even harder, and its attitude began to skew as a new klaxon joined the blare of the other alarms. “That wasn’t me!” Anakin jerked his hands away from the board. “I haven’t even done anything yet!”

“It certainly wasn’t.” Palpatine’s voice was unnaturally calm. “It seems someone is shooting at us.”

“Wonderful,” Anakin muttered. “Could this day get any better?”

... [shortly afterwards]

“Perhaps we can talk with them.” Obi-Wan moved over to the comm station and began working the screen. “Let them know we’ve captured the ship.”

“All right, take the comm,” Anakin said. He pointed at the copilot’s station. “Artoo: second chair. Chancellor?”

“You have to stand down the surface-defense system, sir! It’s General Kenobi!” Needa insisted. “His code verifies, Skywalker is with him-and they have Chancellor Palpatine!”

“Heard and understood this is,” the Jedi [Yoda] responded calmly.

Answer 2

Ever proposing alternative theories...

Does the crew of the fireship CARE whose flying the ship? You have a multi-thousand/hundred/(trillion?) ton vessel, burning, full of volatile fuel and ammo, about to crash into a planet that is literally nothing but one massive city.

Regardless of who is on the ship, they are going to try to help direct to a (relatively) safe landing location, while preventing it from exploding violently all over the sky.

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It's been suggested that the droids on the ship pose a great threat then the ship exploding does, so let's look at some rough numbers.

Coruscant allegedly has the same orbital patterns as Earth, so for simplicity sake we're going to treat is as a similar size (say, 510.1 trillion square meters). Coruscant also has > 1 trillion citizens, divided by the surface area of earth, we end up with about (I'm rounding generously here) 500 people per square meter. Now, this is an inaccurate number because of things like Poles and Oceans and sky ways (which are likely less densely packed then the buildings).

A Nuclear Bomb has a 50% survivability rating at 8 KM. We'll halve that, to 4 KM, just for fun, which comes out to 4000000m² x Population Density of 500 for a grand total of 2,000,000,000 people dead. And taking half of that number again, out to 8km for a whopping total of around 3,000,000,000 dead people if the ship explodes with the same force as a nuclear bomb.

The Invisible Hand carries 1.5 million battle droids, 3,000,000,000 / 1,500,000 = 2. Each battle droid would have to kill 2000 people before being destroyed. Given both their (limited) combat capabilities and their frailness, this seems highly unlikely.

And, in order to achieve this feat, we can go back to the original population density numbers: They would still have to exterminate every living soul within 4 KM of the crash site to accomplish this. It is highly unlikely they would be able to accomplish this before enough military forces were mobilized against them to stop them.

But let's assume it is within the realm of possibility - wouldn't it STILL be better for the ship to land somewhere, you know, with a big wide open area around it, with no cover for the battle droids, so you could easily pick them off as they are disgorging from the ship?

Sort of like they do, in the movie?

This is in fact exactly what Spitfire pilots in World War II did with the buzz bombs that were striking England, tipping them over the countryside or the channel so they would fall out of the sky and crash, and kill less people and cause less damage then if they continued to the target and exploded.

Answer 3

Just to build a little on the other answers. I recall this two line exchange in the movie as being the only communication from the ship after our heroes (And the Chancellor and Anakin) take control (control being a loosely applied term):

Fireship Pilot: "We'll take you in."

Obi-Wan: "Copy that."