Yes, it is still in the solar system. Halley is one of those comets with orbits in the planetary system.
It's periodic returns demonstrates that is was in orbit around the sun and that some comets are members of the solar system. Halley's expected reurn to the inner solar system is the year 2061. Neptune is the planet nearest. One may still think Pluto is an acceptable answer...
Halley's comet orbits the sun roughly once every 76 years. It comes very close to the surface of the Sun on its closest approach. Estimate the greatest distance of the comet from the sun. Is it still in the Solar System? What planet's orbit is nearest when it is out there?
3 answers
Halley's expected return....
They want you to use Kepler's Third Law and the 76 year period to estimate the gretest distance of Halley from the sun. Using that Law will get you the semimajor axis distance (a), which in this case is about half the farthest "aphelion" diatance, since it comes very close to the sun.
P^2/a^3 = 1 is Kepler's third law for bodies orbiting the sun.
a^3 = (76)^2 = 5776
a = 17.9
2a (the maximum distance from the sun) = 35.8 a.u.
P is in years and a is in astronomial units (a.u.).
The average distance of Pluto from the sun in about 44 a.u.
P^2/a^3 = 1 is Kepler's third law for bodies orbiting the sun.
a^3 = (76)^2 = 5776
a = 17.9
2a (the maximum distance from the sun) = 35.8 a.u.
P is in years and a is in astronomial units (a.u.).
The average distance of Pluto from the sun in about 44 a.u.