Why should planets and stars and black holes have all the fun?
Gravity, Gravity, all God’s chillun got Gravity. I know there’s no gravitational “zero-spot” by definition, but isn’t it possible for a 75 kg lump to have its own satellites? Are there any?
Is one Lagrangian point over another a good “zero-spot” if certain (I have no idea) conditions are met? (Good NASA edu site on Lagrangian points: www-spof.gsfc.nasa.gov/Education/wlagran.html.)
I’m pretty sure Newtonian physics scale downward, so yeah, sure, you could have satellites.
However, I suspect to be captured by the gravity of a 75 kg object, they’d be extremely small, and you’d have to be in a vacuum to have it happen, because air currents might waft them away.
It’s certainly possible for a 75-kg lump to have satellites, at least in principle. If we tried to put a small mass in orbit around you in deep space, with an orbital distance of about 5 m (say), it would take about 11.5 days to orbit you. Better pack a lunch. (Also, I’m assuming for this calculation that you’re perfectly spherical, so if you could kind of roll up into a ball, that would be great.)
As far as the Lagrange points go, I’m not sure that you’d need to get to one of those to perform this exercise; my gut instinct is that you just need to get into a free-fall orbit somewhere in the Solar System. I’ll have to think on this some more and get back to you.
This article Hill sphere - Wikipedia gives information about how to calculate how far you’d have to be from any other objects, in order for something to orbit you without it’s orbit being disrupted.
Lil’ Neville was orbiting me when I picked her up from day care this evening- running in circles around me. You could just pick an energetic toddler up from day care… 
There are asteroids with satellites.
Yeah, but she was in a powered trajectory. That’s a little different.
I’m also a bit more massive now, with being pregnant. I feel like I’m up to a solar mass or two.
If you run the numbers, your Hill sphere would extend out about 5 meters so long as you’re farther about 0.14 AU out from the Sun. (And, of course, you’d need to be far enough away from any planets as well.)
Soviet Russia?
The thing with the L4 and L5 points, as I remember, is that even if there aren’t massive bodies there, the gravity influence of the 2 primaries (such as the Earth and moon) can make other objects ‘orbit’ the points. So if the OP was exactly at L5, then he could have much heavier objects orbiting him, but not because of his own gravity.
How dense are you?
Reminds me of a yo mama joke.
Yo mama’s so dense, her head has an event horizon!
There are things sort of orbiting you, since you’re on Earth and your mass contributes to it’s gravity.
I should clarify this. I mean that the Moon, smaller bodies, artificial satellites, etc. are orbiting you.
So if your Hill sphere extends out 5 metres, ant you place a grain of salt three meters out from your equator, what would be its orbital velocity?
For a circular orbit, and assuming that you’ve rolled yourself up into a nice spherical mass: 41 microns per second, corresponding to an orbital period of 5.3 days. (This assumes your mass is the 75 kg listed above.)
Your answer is philosophy.
Solipsism. I am the center of the universe, and everything moves relative to me. Even if it doesn’t look like it’s orbiting me, add enough epicycles to the model and you’ll discover it does.
The geocentric and heliocentric models of the universe are mathematically equivalent. There’s no reason the “me-o-centric” model can’t be as well.
Also, not only does the universe orbit around me, it exists because I decide it exists.
Well, you could just choose a reference frame where you’re stationary and the rest of the universe orbits around you. Doing physics would be complicated, as it’s not an inertial reference frame, and you’d need lots of fancy math and funny physics. But, there’s no law against it.