We discover a nearby star with two planets. the first planet has an orbit period of 10 years and is in a circular orbit with radius 106 km. the second planet has an orbit period of 15 years. what is its orbit radius? you may assume it is also in a circular orbit.

Assuming the given radius is 10⁶ km, the radius of the second planet is 1.31 * 10⁶ km.

Explanation:

Newton's law of gravity:

(1)

Centripetal force:

(2)

On a circular orbit both forces must be equal:

(3)

Solving for ω:

(4)

The period T is given by:

(5)

Taking the ratio of two periods:

(6)

Solving for r₁:

(7)

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.