How far would the planet be from the sun if...

Question

Asteroids are believed to be material that never collected into a planet. An asteroid has a period of 6.8 years. Assuming the asteroid to be at the center of the planet if it had formed, how far would the planet be from the Sun? 
_____ AU

Answer 1

Use Kepler's 3rd Law:

 

P_a²          D_a³

-------  =  --------

P_e²          D_e³

 

Where:

• Pa = the orbital period of the asteroids = 6.8 years
• Pe = Earth's orbital period = 1 year
• Da = the distance of the asteroid planet from the sun in astronomical units (AU)
• De = the distance of Earth from the sun = 1 AU

 

(6.8)²      D_a³

-------- = ----------

 1²            1³

 

46.24 = D_a³

 

³√(46.24) = D_a

 

3.59 AU = D_a