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?
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.
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...
Well, Halley's comet sure knows how to make an impression by getting up close and personal with the Sun! When Halley's comet is at its closest approach to the Sun, also known as perihelion, it comes within about 0.6 astronomical units (AU) of the Sun. Since 1 AU is the average distance between the Earth and the Sun, that means it gets only about 56 million miles away from our favorite fiery ball of gas.
Now, is Halley's comet still in the Solar System? Absolutely! In fact, the comet's orbit takes it pretty far out, beyond the orbit of Neptune, the farthest planet from the Sun. Talk about an adventurous comet!
As for the planet nearest to Halley's comet when it's out there, it can come quite close to Venus during certain points in its orbit. So, if you happen to catch Halley's comet during that time, you might just have a glimpse of Venus gracefully waving hello as it passes by.
To estimate the greatest distance of Halley's comet from the Sun, we can use its orbit's eccentricity. Halley's comet has an eccentric orbit, meaning it is not perfectly circular. The greatest distance from the Sun, also known as the aphelion, can be calculated by multiplying the perihelion distance (closest approach to the Sun) by a factor of 1 plus the eccentricity.
The perihelion distance of Halley's comet is about 0.59 astronomical units (AU), where 1 AU is the average distance from the Earth to the Sun (approximately 93 million miles or 150 million kilometers). The eccentricity of Halley's comet is approximately 0.97.
Using the formula: aphelion = perihelion × (1 + eccentricity), we can calculate the greatest distance:
aphelion = 0.59 AU × (1 + 0.97) = 0.59 AU × 1.97 = 1.163 AU
Therefore, the estimated greatest distance of Halley's comet from the Sun is approximately 1.163 AU.
Yes, Halley's comet is still considered part of the Solar System. Its orbit extends well beyond the orbit of Pluto, the farthest known planet in our solar system.
When Halley's comet is out there, it can come close to the orbits of several planets, including Earth, Mars, Venus, and Mercury. However, the planet whose orbit is nearest to Halley's comet when it is out there is Venus.