People cite circumstantial evidence that there is some planet:
but otherwise unlocated.
Where to look?
I have an idea.
I suggest four small, low power, space craft deployed at perhaps 10 AU from the Sun forming a crude regular tetrahedron with edge about 16 AU.
After deployment they would dispose of their thrusters dedicating themselves to move under the exclusive force of gravity.
They would take extraordinary precautions to limit their angular momentum just before discarding their thrusters.
They would carry lasers capable of trading signals conveying time to less than a nanosecond.
Their charter is to report 6 distances three times spread over several years.
They would report those time to Earth where we would compute their orbits with unprecedented accuracy.
The tidal force of the new planet should make itself evident.
That should identify a direction in which to look.
- in our solar system,
- about 10 time the mass of the Earth,
- Well beyond Pluto,
- Highly eccentric orbit.
- Orbit out of the plane of the other planets.
The Good News
These system sleep most of the time; they need a clock only a little better than my wrist watch which does not sleep.Their science phase is probably less than an hour of power and not a lot (I hope) of laser energy.
They have motors that can be turned on to direct the laser to one of the other crafts.
The Bad News
The other forces must be known: photons from
We may need a better model of the astroid belt.
- the Sun striking the craft,
- the craft
We would learn the shape of the tetrahedron to 12 digits but know its orientation (O(3)) from those 4 edge lengths much less accurately, about 8 digits.
We have three degrees of freedom for those 4 extra digits.
The four craft can each do a range check with a well positioned Earth satellite.
Now some numbers: