The orbit of a planet is surrounded by a chaotic zone wherein nearby particles ’ orbits are chaotic and unstable .
Wisdom ( 1980 ) showed that the chaos is driven by the overlap of mean motion resonances which occurs within a distance ( \delta a / a ) _ { \mathrm { chaos } } \approx 1.3 \mu ^ { 2 / 7 } of the planet ’ s orbit .
However , the width of mean motion resonances grows with the particles ’ eccentricity , which will increase the width of the chaotic zone at higher eccentricities .
Here we investigate the width of the chaotic zone using the iterated encounter map and N-body integrations .
We find that the classical prescription of Wisdom works well for particles on low-eccentricity orbits .
However , above a critical eccentricity , dependent upon the mass of the planet , the width of the chaotic zone increases with eccentricity .
An extension of Wisdom ’ s analytical arguments then shows that , above the critical eccentricity , the chaotic zone width is given by ( \delta a / a ) _ { \mathrm { chaos } } \approx 1.8 e ^ { 1 / 5 } \mu ^ { 1 / 5 } , which agrees well with the encounter map results .
The critical eccentricity is given by e _ { \mathrm { crit } } \approx 0.21 \mu ^ { 3 / 7 } .
This extended chaotic zone results in a larger cleared region when a planet sculpts the inner edge of a debris disc comprised of eccentric planetesimals .
Hence , the planet mass estimated from the classical chaotic zone may be erroneous .
We apply this result to the HR 8799 system , showing that the masses of HR 8799 b inferred from the truncation of the disc may vary by up to 50 % depending on the disc particles ’ eccentricities .
With a disc edge at 90 AU , the necessary mass of planet b to cause the truncation would be 8–10 Jovian masses if the disc particles have low eccentricities ( \lesssim 0.02 ) , but only 4–8 Jovian masses if the disc particles have higher eccentricities .
Our result also has implications for the ability of a planet to feed material into an inner system , a process which may explain metal pollution in White Dwarf atmospheres .