# NEO trajectory math.

Started by
Mister T
, Jan 11 2013 10:39 AM

4 replies to this topic

### #1

Posted 11 January 2013 - 10:39 AM

I am constantly in awe of the mathematical computations used to project orbits and "fly-bys" of NEO's.

The degree of accuracy must be, for a lack of a better term, Astronomical.

As an example, what kind of accuracy was required to determine that Shoemaker Levy 9 was going to hit Jupiter on it's next pass?

Also, How much of the computations involve gravitational influences of the sun and planets and moons?

I am thinking it is roughly equivalent to shooting a BB at a beach ball from across the ocean. (just a guess)

The degree of accuracy must be, for a lack of a better term, Astronomical.

As an example, what kind of accuracy was required to determine that Shoemaker Levy 9 was going to hit Jupiter on it's next pass?

Also, How much of the computations involve gravitational influences of the sun and planets and moons?

I am thinking it is roughly equivalent to shooting a BB at a beach ball from across the ocean. (just a guess)

### #2

Posted 11 January 2013 - 10:50 AM

The math is pretty straight forward. You compute the orbit and take into consideration any 'near passes' to gravitational attractive planets that can influence the orbit and project out from there.

The trick is you need to know precisely where an object is and its exact mass -and that is not the easiest thing to find. A tiny error at the start can amplify into millions of miles after several orbits.

That's why you hear, 'A NEO object has the potential to to Hit Earth in the year 2075' or something to that effect. They project out the orbit and the farther they go the more the error brackets enlarge. What they are saying is that at some point in their margin of error the Earth could coincide in orbit with the NEO.

Pesse (It's a great headline but if the error brackets extend from Venus to Mars...?) Mist

The trick is you need to know precisely where an object is and its exact mass -and that is not the easiest thing to find. A tiny error at the start can amplify into millions of miles after several orbits.

That's why you hear, 'A NEO object has the potential to to Hit Earth in the year 2075' or something to that effect. They project out the orbit and the farther they go the more the error brackets enlarge. What they are saying is that at some point in their margin of error the Earth could coincide in orbit with the NEO.

Pesse (It's a great headline but if the error brackets extend from Venus to Mars...?) Mist

### #3

Posted 11 January 2013 - 11:20 AM

The mass of the object doesn't matter so much unless it is big enough to have significant influence on the sun or planets. What you need to know precisely are its location and velocity vector.

For objects that are far apart (like the planets from each other), you can calculate their orbits out a long way very accurately. This is because gravity works by the inverse square of the distance - when you objects are far apart, the change in gravity is small per unit distance, so even if your estimate of position is off a bit, it doesn't change the prediction much.

Close passes are a different matter - when something is passing close to a massive object, small changes in location turn into big changes in gravity and velocity. So predicting orbits after one of those either requires that you get really precise measurements ahead of time, or wait until after the close pass and see what happens.

Jarad

For objects that are far apart (like the planets from each other), you can calculate their orbits out a long way very accurately. This is because gravity works by the inverse square of the distance - when you objects are far apart, the change in gravity is small per unit distance, so even if your estimate of position is off a bit, it doesn't change the prediction much.

Close passes are a different matter - when something is passing close to a massive object, small changes in location turn into big changes in gravity and velocity. So predicting orbits after one of those either requires that you get really precise measurements ahead of time, or wait until after the close pass and see what happens.

Jarad

### #4

Posted 11 January 2013 - 02:17 PM

Celestial Mechanics is both straightforward and maddenly chaotic. The difficulty comes when trying to model multiple bodies over long periods of time. There are at least a dozen modelling schemes out there, each with differing degrees of accuracy, speed, and computational demands.

N-body codes

Fortunately, the trajectory of encounters such Shoemaker-Levy-9 involve relatively few bodies and short time scales, so the numerical methods available can make quick work of its path.

N-body codes

Fortunately, the trajectory of encounters such Shoemaker-Levy-9 involve relatively few bodies and short time scales, so the numerical methods available can make quick work of its path.

### #5

Posted 11 January 2013 - 05:09 PM

Imagine what it was like back in the slide-rule era and earlier -- before Dr. Paul Herget at the University of Cincinnati/Cincinnati Observatory/Minor Planet Center got his hands on a Univac (or was it Eniac?).