When a planet moves around the sun

• A. The angular momentum remains conserved
• B. The angular speed remains constant
• C. The linear velocity remains constant
• D. The linear momentum remains constant

Answer: (A)

When gravity acts as the only force on a planet, it is a central force directed along the line from the planet to the sun. That means the torque about the sun is zero (r × F = 0), so the angular momentum about the sun is conserved. The angular momentum is L = m r^2 dθ/dt, which stays constant as the planet moves along its orbit. As the planet gets closer to the sun, it must sweep through angle more quickly to keep L the same; as it moves farther away, its angular speed decreases. The linear speed and linear momentum do change because the gravitational force does work on the planet, converting between kinetic and potential energy. But the quantity that remains constant is the angular momentum, making that option the correct statement.