Consider a planet and an asteroid in the solar system. Both their orbits can be considered as a circle. Their distance to the center of the sun differ by a factor of 4. rB = 4 rA
When r increases by a factor of 4, how do period T, angular velocity , and linear speed v change respectively?
Hint: If you remember how r and (or T) are related, you can use that relationship directly. If you forget, you can consider that the gravitational force received from the sun equals the centripetal force needed to derive the relationship between r and .
1. [tex]T_{B}[/tex] = ___ [tex]T_{A}[/tex]
[tex]\omega_{B}[/tex]=___[tex]\omega_{A}[/tex]
[tex]v_{B}[/tex] = ___[tex]v_{A}[/tex]