Just a little quick math.<br><br>When Jupiter and Earth are aligned on the same side of the Sun, they are on average 4.2 Astronautical Units (AU) apart.<br><br>When Pluto and Earth are similarly aligned, they are 38.5 <br>AU apart.<br><br>Since gravity attenuates as the square of the distance, if this planet were only in Pluto orbit, it would have to have 81 times the mass of Jupiter to have the same, tiny, gravitational effect that Jupiter has on Earth.<br><br>However, since Pluto has a "year" that is 248.54 Earth years long, we can estimate that this other planet, with its 3650 Earth year orbit, is at least 10 times as far out as Pluto, thus it would have to mass 100x81 times Jupiter to have the same, tiny effect of Jupiter.<br><br>This would give it a mass of about 7 times that of the Sun.<br>I think that it would be sort of hard to hide, since I think that with that kind of mass it should be alight.