Kepler's Laws Govern Orbital Speed and Period

Steps:

• Kepler's third law states T² ∝ r³, so T increases with orbital radius r.
• Jupiter's larger r means its T exceeds Earth's T.
• Orbital speed v = √(GM/r) for circular orbits, so v decreases as r increases.
• Earth's smaller r gives it higher v than Jupiter.

Why B is correct:

• B matches v_Earth > v_Jupiter (from v ∝ 1/√r) and T_Jupiter > T_Earth (from T ∝ r^{3/2}).

Why the others are wrong:

• A: Incorrectly assigns larger T to Earth, ignoring Kepler's third law.
• C: Wrongly gives Jupiter larger v, contradicting v decreasing with r.
• D: Falsely claims Jupiter has larger v and Earth larger T.

Final answer: B