Answer:
103239.89 days
Explanation:
Kepler's third law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
a³ / T² = 7.496 × 10⁻⁶ (a.u.³/days²)
where,
a is the distance of the semi-major axis in a.u
T is the orbit time in days
Converting the mean distance of the new planet to astronomical unit (a.u.)
1 a.u = 9.296 × 10⁷ miles
[tex]\frac{4004 * 10^{6}}{9.296 * 10^{7}} = 43.07\ a.u.[/tex]
Substituting the values into Kepler's third law equation;
[tex]\frac{(43.07)^{3}}{T^{2}} = 7.496 * 10^{-6}[/tex]
[tex]T^{2} = \frac{(43.07)^{3}}{7.496 * 10^{-6}}[/tex] (days)²
[tex]T^{2} = \sqrt{\frac{(43.07)^{3}}{7.496 * 10^{-6}}}[/tex]
T = 103239.89 days
An estimate time T for the new planet to travel around the sun in an orbit is 103239.89 days
