Question

Between the orbits of Earth and Mars, there is a region of space that is filled with a large number of asteroids. One of the objects within this asteroid belt is the dwarf planet Ceres. Ceres orbits the Sun in an approximately circular orbit with a radius about 2.7 times larger than the radius of Earth’s orbit. Is the time that it takes Ceres to orbit the Sun more than 2.7 years, equal to 2.7 years, between 1 year and 2.7 years, or less than 1 year?

Answer 1

Radius of orbit of Ceres, Rc = 2.7 Re where Re is the orbital radius of earth

Time period of revolution of earth, Te = 1 year

Let Tc be the time period of revolution of Ceres.

From Kepler’s 3rd law of planetary motion,

T2 α R3

(Tc/Te)2 = (Rc/Re)3 = (2.7 Re/Re)3 = 2.73 = 19.683

Tc/Te = 19.8631/2 = 4.44

Tc = 4.44 Te = 4.44 x 1 = 4.44 years

time period of revolution of Ceres, Tc = 4.44 years.

Answer: the time that it takes Ceres to orbit the Sun is more than 2.7 years