Question

an asteroid is 3 times as far from the sun as the earth. what is it's period in earth years?

Answer 1

Question #31973

an asteroid is 3 times as far from the sun as the earth. what is it's period

in earth years?

Solution

According to the third Kepler's law

"The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."

$$\frac {P _ {\text {a s r t e r o i d}} ^ {2}}{a _ {\text {a s t e r o i d}} ^ {3}} = \frac {P _ {\text {e a r t h}} ^ {2}}{a _ {\text {e a r t h}} ^ {3}}$$ $$P _ {a s r t e r o i d} = \sqrt {\frac {P _ {e a r t h} ^ {2} * a _ {a s t e r o i d} ^ {3}}{a _ {e a r t h} ^ {3}}} = P _ {e a r t h} \sqrt {\frac {a _ {a s t e r o i d} ^ {3}}{a _ {e a r t h} ^ {3}}}$$

Such as

$$a _ {a s t e r o i d} = 3 a _ {e a r t h}$$ $$P _ {a s r t e r o i d} = P _ {e a r t h} \sqrt {3 ^ {3}}$$ $$P _ {a s r t e r o i d} \approx 5. 2 P _ {e a r t h} \approx 5. 2 y e a r s$$

Answer:

The period is 5.2 earth years. (5 years 73 days)