91影视

The relation between the mean distance and period of two item鈥檚 is shown by the Kepler鈥檚 third law. Mathematically, it can be written as,

\({r_1} = {r_2}{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^{\frac{2}{3}}}\)

Here, \({r_1}\) and \({r_2}\) are the mean distance, and \({T_1}\) and \({T_2}\) are the periods.

The period of Halley鈥檚 comet is \({T_H} = 76\;{\rm{years}}\).

The period of Earth is \({T_E} = 1\;{\rm{years}}\).

The distance of Earth is \({r_E} = 1.5 \times {10^8}\;{\rm{km}}\).

From Kepler鈥檚 third law.

\(\begin{aligned}{r_H} &= {r_E}{\left( {\frac{{{T_H}}}{{{T_E}}}} \right)^{\frac{2}{3}}}\\{r_H} &= \left( {1.50 \times {{10}^8}\;{\rm{km}}} \right){\left( {\frac{{76\;{\rm{years}}}}{{1\;{\rm{years}}}}} \right)^{2/3}}\\{r_H} &= 2.69 \times {10^8}\;{\rm{km}}\end{aligned}\)

This is the semi-major axis.

The greatest distance of comet from the sun can be calculated as,

\(\begin{aligned}D &= 2{r_H}\\D &= 2\left( {2.69 \times {{10}^9}\;{\rm{km}}} \right)\\D &= 5.38 \times {10^9}\;{\rm{km}}\end{aligned}\)

Thus, the greatest distance of the comet is \(5.38 \times {10^9}\;{\rm{km}}\).

Yes, the comet is still in the solar system nearest to Pluto's orbit because distance \(D\)approaches the mean orbit distance of Pluto which is \(5.9 \times {10^2}\;{\rm{m}}\).

Thus, the mean orbit distance of Pluto which is \(5.9 \times {10^2}\;{\rm{m}}\).