Question

Most asteroids are found between 2.1 and 3.3 AU. Use Kepler's third law to calculate the range of orbital periods associated with these orbital sizes

Answer 1

Answer on Question #48038, Physics, Astronomy — Astrophysics

Most asteroids are found between 2.1 and 3.3 AU. Use Kepler’s third law to calculate the range of orbital periods associated with these orbital sizes

Solution

Use Kepler’s third law tells us that expression

$\frac{P^{2}}{a^{3}}$

is the same for all planets, where $P$ is period and $a$ is distance. Hence, for $a_{2}=2.1$ and $a_{3}=3.3$ AU we have periods

$P_{2}=P_{1}\frac{a_{2}^{3/2}}{a_{1}^{3/2}},\quad P_{3}=P_{1}\frac{a_{3}^{3/2}}{a_{1}^{3/2}}$

$P_{2}=1yr\cdot\frac{2.1^{3/2}}{1^{3/2}}\approx 3\,yr,\quad P_{3}=1yr\cdot\frac{3.2^{3/2}}{1^{3/2}}\approx 5.7\,yr$

http://www.AssignmentExpert.com/