How do astrophysicists predict the orbit of planets?

Question

How do astrophysicists predict the orbit of planets?

Answer 1

Well x,y,z, and t is four coordinates, not two. But yes with those measurements done at different times you can easily figure out how long it took a planet to move between the two points. Throw in some orbital dynamics and figuring out the rest of the orbit isn't that hard. Of course just two seperate measurements wouldn't give you an absolute 100% model of the orbit. Just a basic mapping of it. More measurements would need to be made at different times to get it exact.

Answer 2

Six quantities are needed to determine the orbit of an object. There are the classical equations which require 6 known variables concerning the shape, size and orientation of the orbit and the object's location at any time. The method used today is numerical integration with the coordinates x, y, z and the velocities x', y', z' being the 6 starting quantities. So your two sets of coordinates is equivalent, provided the time interval between them is short.



Predicting the orbits of planets in the solar system is an n-body problem, where all other perturbing bodies have to be taken into account. From observations, the rectangular coordinates (x, y, z) and velocities (x', y', z') are determined for the starting time. Then a step by step process is undertaken. Using a suitable interval (day, hour, etc.) integrate the velocity to determine the distance moved. Integrate the total acceleration from all other bodies (calculated by the inverse square law - a function of the separation of each body, easily calculated) to obtain the new velocity. Now each body is at a new position with a new velocity, so just repeat the process.



The method has long been known and is very simple, but was impractical before the advent of fast electronic computers some 60 years ago.

Answer 3

Yes, two sets of {x,y,z} position coordinates at two times is enough. Actually, you also need the sun's mass. That's ignoring the effect of all the other planets. In the case of Mars, you also need to include the effect of the asteroids.



But .. in practical terms, nobody does it that way. We use angle observations of the outer planets. For the inner planets we have radar and space probes to give us the distances. Then all the observations, thousands of them, are tossed into a giant computer program. This figures out the obits that best matches the observations. The program also figures out the mass of the Sun, moon, and planets.

Answer 4

"...Specifying orbits Main article: Orbital elements

Six parameters are required to specify an orbit about a body. For example, the 3 numbers which describe the body's initial position, and the 3 values which describe its velocity will describe a unique orbit that can be calculated forwards (or backwards). However, traditionally the parameters used are slightly different.



The traditionally used set of orbital elements is called the set of Keplerian elements, after Johannes Kepler and his laws. The Keplerian elements are six:



Inclination (i)

Longitude of the ascending node (Ω)

Argument of periapsis (ω)

Eccentricity (e)

Semimajor axis (a)

Mean anomaly at epoch (M0)

In principle once the orbital elements are known for a body, its position can be calculated forward and backwards indefinitely in time. However, in practice, orbits are affected or perturbed, by other forces than simple gravity from an assumed point source (see the next section), and thus the orbital elements change over time. ...."



http://en.wikipedia.org/wiki/Orbit



Mathematical equation just don't paste into YA, so you'll actually have to open the links. There's a section above the one quoted in the same Wikipedia article with mathematical equations.



"...Orbit prediction Under ideal conditions of a perfectly spherical central body, and zero perturbations, all orbital elements, with the exception of the Mean anomaly are constants, and Mean anomaly changes linearly with time, scaled by the Mean motion, .[2] Hence if at any instant the orbital parameters are , then the elements at time is given by



[edit] Perturbations and elemental variance Unperturbed, two-body, Newtonian orbits are always conic sections, so the Keplerian elements define an ellipse, parabola, or hyperbola. Real orbits have perturbations, so a given set of Keplerian elements accurately describes an orbit only at the epoch. Evolution of the orbital elements takes place due to the gravitational pull of bodies other than the primary, the nonsphericity of the primary, atmospheric drag, relativistic effects, radiation pressure, electromagnetic forces, and so on.



Keplerian elements can often be used to produce useful predictions at times near the epoch. Alternatively, real trajectories can be modeled as a sequence of Keplerian orbits that osculate ("kiss" or touch) the real trajectory. They can also be described by the so-called planetary equations, differential equations which come in different forms developed by Lagrange, Gauss, Delaunay, Poincaré, or Hill. ..."



http://en.wikipedia.org/wiki/Orbital_elements





This article gives the mathematical equations. Good luck in understanding it. It really does help in understanding the equations if you've taken at least THREE semesters of calculus.