So we can determine the orbit using only line of sight measurements of the object relative to the Earth.

This is a problem originally solved by Gauss for Ceres.

https://en.wikipedia.org/wiki/Gauss%27s_method

More generally given sufficient observations one can use many similar methods of orbit determination to get a relatively accurate orbit of the body. All of this is standard stuff in astrodynamics and happens on a near constant basis for both man made and natural objects.

A good introduction is the classic BMW

https://www.amazon.com/Fundamentals-Astrodynamics-Dover-Aero...

None of this requires the shape or material of the object, just some fuzzy measurements of the position

But surely it can be affected if the body outgasses because of some solar effect? I don't believe that applies to Ceres, or to satelites around the Earth, etc.

Outgassing should be seen. If it is close enough to the sun to melt anything, it is close enough that we should see the resulting tail. Once it is far away from the sun again, outgassing should stop as everything freezes up.

That depends quite highly on the object's mass.

The trajectory of an object in space really only depends on the (external) gravitational field applied to it.

No, it also depends on effects like the pressure from the solar wind and outgassing. Outgassing is caused by water on the side facing the sun evaporating, emitting a gentle pressure away from the sun. If the object is rotating, the force pushes at an angle to the sun because the outgassing rate lags insolation due to the surface water's thermal mass (ie, each point on the surface continues to evaporate for a while after its apparent sunset.)

The effects aren't significant for planets, but they are for asteroids. It seemed more significant for Oumuamua than most, suggesting a high surface area to volume ratio.

I thought outgassing and solar wind was only really relevant when applied for a long time over many periods of an orbit? Would it have a significant impact on a one-time hyperbolic trajectory like this one?

In fact, one of the things proposed in the article is that the object is a light sail being accelerated by the sun.

And its speed!

Well, yes. I guess I was talking more on the lines of acceleration and deviations from a straight line trajectory :)

I think the projected trajectory is the path expected without some unknown force acting on it.

Yes, but here's my problem with expected trajectory being used as evidence of aliens, and 'unknown force' being used as some mysterious alien technology.

If I remember right, one of the voyager or pioneer probes was moving much faster than it should've been (relatively), and we had no idea why for years. Then we figured out it was the cumulative effect of heat radiation(?) from something on board the machine.

If we can't figure out what WE made, how can we expect to figure out a once-in-a-generation event like this on the first shot?

rate of acceleration was more in line with object offgassing due to irradiation from the sun, at least as what I got from scientific sources last year.