Reasonable way to determine orbital parameters in an unknows stellar system

Question

After traveling a long long time, your spaceship is finally entering into the gravitational sphere of influence of a Sun-like star. Your captain would now like to move from the Oort-like cloud distance where the ship is moving after entering the system to the inner depths of the system itself, possibly avoid slamming onto an un-spotted Jovian gas giant or a an asteroid belt (not even mentioning the main star) because of some unexpected Gravitational pull along the trip. Your ship's insurance provider, despite appreciating scientific effort, does not approve using the ship itself as a probe.

Now you, as navigation engineer, want to determine the best set of orbital parameters to explore the system without using too much fuel, but still you don't know:

• how many planets there are
• how massive they are
• which orbits they follow

Is there any way to find these info from your standpoint and possibly quicker than spending few hundreds years observing the sky, like your ancestors did on planet Earth?

You have no magic. Only nowadays technology (except the part allowing you to do interstellar cruise...)

Answer 1

Some things will require planet-hopping

The easy way to find planets is to simply film all of the starry the starry sky, while traveling along a known trajectory. Eddie — your friendly Sirius Cybernetics shipboard computer — will analyze the movements of all the bright dots, and if any of them move in relation to others, then you know this is a planet. From this it is fairly routine trigonometry for Eddie to find the positions of the different planets.

Keep doing this for a while, say an hour or so and Eddie will keep plotting the positions of the planets. From this Eddie finds out the velocity, that is to say the speed and direction of the planets. With this Eddie will quickly calculate the orbital parameters of the different bodies in the system.

Calculating the size of the different bodies is just a matter to putting your shipboard telescope on them. Using the measured size and the appearance of the planets you can approximate the mass. Eddie can do this for you as well. You will end up within the correct magnitude, even if you may be off by a few hundred percent.

To get an accurate measurement of the mass of the bodies however, you need to get fairly close to them and use your gravimeter. Start with the star itself, then you will have to go planethopping, getting close enough to each so that you can approximate that the other planets' respective gravity will not be significant during your measurements.

And like so you have what you asked for. Share and Enjoy!

After question edit

One thing that is worth to notice is that space is big. Really big. You just won't believe how vastly, hugely mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space! Listen...

...and so on.

The point is that the risk that you will run head first into a planet is negligible. Sure, Jupiter and Saturn are gigantic balls of obstacle-ness that will do very bad things to your spacecraft should you drive it straight into them, but compared to space itself they are really tiny.

If you wish to mitigate this (non-)risk the answer is still the same: keep filming the sky — preferably in infrared — and be on the lookout for "stars" that move. Objects as huge as Jupiter will be visible well in time for you to take evasive action. And if you wish for even more risk mitigation, send a little remote controlled drone ahead by a few hours, letting that do the job, and follow in its footsteps.

Answer 2

Arriving in the Oort cloud gives you a long time to search for planets

If you start into the Oort cloud, it is going to take you 10s if not hundreds of years to get into the inner solar system. Comets that travel as far out as the Oort cloud are long-period comets often with orbits in the thousands of years.

If you want to get into the inner solar system faster, then you have to use your engines to give you more velocity than a simple orbital velocity. If you arrive in the inner Oort cloud (or Hills cloud), you are still at least 100 AU, and possibly as much as 3,000 AU from the central star. If you arrive in the middle of the Hills cloud then you are maybe 10,000 AU from the central star.

Light travels 1 AU in 500s, so at 0.1c, it takes 5000s to go 1 au. That means from 3,000 AU out, it takes 173 days to get into the inner solar system. This is plenty enough time to use on-board optical equipment to detect any and all planets, as detailed by Michael Karnerfors. Even at such a great speed as 0.1c, if you concentrate your sensors in the direction of your travel you should be able to resolve objects the size of, say, Pluto from the same distance away as Pluto from Earth (variable, but lets say 30 AU as a rough minimum). If you can see Pluto 30 AU away, then you have 30*5000 = 42 hours to avoid hitting it. Serious obstacles like Jupiter should be visible as soon as you arrive in the system.

The chances of collision with smaller objects is almost statistically negligible, but probably hard to avoid if you are moving at 0.1c. That is just a risk you will have to take; but then that is a risk that all of our outer solar system probes are taking. The chances of hitting an object in the vastness of the solar system are pretty small.

In conclusion, set yourself on a hyperbolic orbit like a long-period comet, switch on all your sensors to keep an eye on where you are going, and map the solar system was you go. Since it is going to take your on a time scale of years to get to the inner solar system, you have plenty of time to find all the planets by the time you get there.