The asteroid Ceres orbits the Sun like the other planets. Its period is about 16

Question

The asteroid Ceres orbits the Sun like the other planets. Its period is about 1670 days. What is its mean distance from the Sun? (Note: this problem does not involve much calculator use, IF you set up a ratio, and use time-units of days and distance units of AU. 1 AU is the distance from the Earth to the Sun. CAPA will accept units of AU for distance.) The asteroid Ceres orbits the Sun like the other planets. Its period is about 1670 days. What is its mean distance from the Sun? (Note: this problem does not involve much calculator use, IF you set up a ratio, and use time-units of days and distance units of AU. 1 AU is the distance from the Earth to the Sun. CAPA will accept units of AU for distance.)

Explanation / Answer

Kepler's Third Law is T^2/r^2 is a constant for all systems revolving around another

SInce the asteroid and Earth both rotate around the sun, we can set up that proportion using the Earths data

Earths data is 1 AU for radius and 1 year for period

1670 days is 4.57 years, so...

4.57^2/r^3 = 1^2/1^3

4.57^2 = r^3

r = 2.75 AU

That is 4.12 X 10^11 m or 4.12 X 10^8 km

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