You might be thinking that we cannot possibly know, because there's nothing on screen about it. But I think that this is one of those mind-bending puzzles where we seemingly have no information at all but actually we can deduce enough to make some pretty shrewd estimates.

  • We saw two mission time clocks, giving the relative time rates on two decks of the ship.
  • We saw a city with skyscrapers, whose sizes we can estimate from the number of floors.
  • We saw just after the opening titles the approximate height of a deck relative to the skyscrapers.
  • We know the deck numbers.
  • We saw no appreciable tidal effects.

Let's assume general relativity as in the real universe (given than the writers made a plot point out of it), normal sized humans and time lords, and Terran standard days and hours (given the whole Mondas being a twin of Earth thing). Let's also assume common Terran sizes of skyscrapers, if we cannot see all of the windows of any one in order to count them. And let's assume that what we saw of the hospital applies generally: not more than one row of windows per floor.

It seems that we know two points and the distance between them, and the relative rates of time dilation, giving us a gradient; and we also know that tidal effects are weak. We even know that the axis of the ship is perpendicular to the axis of rotation of the black hole, because its accretion disc was shown on screen as observed from the ship.

The ship is clearly under thrust, towards the black hole, and from the alignment of the decks shown just after the opening titles it is implied that artificial gravity is designed to be a product of that thrust. Let's assume a thrust of 1G, which is consistent with what appears on screen.

Can we deduce the mass of the black hole from any or all of this? Or at least bounds upon that mass? If so, what is it? If not, what information do we lack?

  • I recall a line from the janitor on the bridge saying something to the effect that they could not get away and were basically stuck between their trust and the pull of the black hole. – amflare Jul 20 '17 at 20:33
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    The physics shown in the show is at great variance with real physics. As such, your question is off-topic on this stack if you want a proper explanation. – Valorum Jul 20 '17 at 21:33
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    J Doe you need to familiarize yourself with Physics's policy, which specifically excludes physics of fictional universes. Valorum, you need to refresh your memory of scifi.meta.stackexchange.com/a/7367/21871 . This is a question about a science fictional object, based upon what is seen on screen and some fairly reasonable assumptions about what unstated physics we can fill in, that are indeed based upon actual plot points. We are on the right site. – JdeBP Jul 20 '17 at 21:49
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    You are clearly grossly mis-applying it, then. This question does not ask for out-of-universe explanation of physical principles. Indeed, it explicitly states that we take them as read, exactly as the characters in the story do. It asks for the mass of a fictional object, given various things that we are outright told in the story. Like how people ask about the size/mass/atmosphere/satellites of the Death Star, or the time dilation and gravitation in Interstallar, or the mass of the TARDIS; all of which are questions here. – JdeBP Jul 21 '17 at 6:45
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    "Let's assume general relativity as in the real universe" - You're asking for real-world out-of-universe physics to be used, so in fact you are asking for an out-of-universe explanation. If you want it to be in-universe, you have to use in-universe physics. – DisturbedNeo Jul 21 '17 at 9:01

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