Could a rotating Black Hole of mass $1.24\times 10^{10}$ kg maintain a stable orbit around Earth, without significantly altering the path of the Earth or Moon? In addition to this, would the presence of the hole have an effect on the Earth's tides?
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4$\begingroup$ 1. Why that specific mass? 2. The stability of the orbit (and, in fact, almost all of the physics away from the Schwarzschild horizon) doesn't depend on the thing being a black hole at all. $\endgroup$– ACuriousMind ♦Apr 26, 2016 at 19:31
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$\begingroup$ The mass corresponds to other calculations pertaining to its energy output. It would be an upper limit on the mass. $\endgroup$– Noah PApr 26, 2016 at 19:35
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1 Answer
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That's fairly small for an object. It wouldn't have any significant gravitational effect on the moon or the earth.
Tidal effects go as the cube of the distance. So the sun has about half the tidal effects of the moon.
If this object were in low earth orbit (400km altitude), then the relative tidal effects on the surface when it is overhead would be about $\frac{m_{\text{object}}}{m_{\text{moon}}} (\frac{d_\text{moon}}{400\text{km}})^3$ or a bit more than one ten-thousandth that of the moon.
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$\begingroup$ Would it be able to orbit the earth without spiralling inwards? $\endgroup$– Noah PApr 26, 2016 at 20:21
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$\begingroup$ The fact that it's a black hole is irrelevant. To the first order, satellites don't spiral inward; they have elliptical orbits around the primary. Atmospheric drag and tidal drag can cause it to spiral in. The first is minimized by orbiting at a higher altitude. The second is minimal because it's not very large compared to the mass of the earth. $\endgroup$ Apr 26, 2016 at 20:31
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$\begingroup$ Brilliant. Do you know of a good reference available online that I could read up about this a it more? $\endgroup$– Noah PApr 26, 2016 at 20:44
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$\begingroup$ Where do you derive your equation from that is used in the answer? @BowlOfRed $\endgroup$– Noah PApr 27, 2016 at 11:16