Physics · Gravitation · NEET
Because angular momentum L = m·r·v (at perihelion and aphelion, where r and v are perpendicular) stays constant. When the planet is closer, r is small, so v must become large to keep m·r·v the same. So near the Sun (perihelion) the planet is fast, and far from the Sun (aphelion) it is slow. The Law of Areas is just this rule stated in terms of swept area.
They are the same physics. The area swept per unit time is dA/dt = L/2m. Since gravity is a central force (it always points from the planet straight to the Sun), the torque about the Sun is zero, so L is constant. If L is constant, then dA/dt is constant, which is exactly the Law of Areas. This is why the law works for ANY central force, not just gravity.
No. dA/dt (the area swept per second) is constant, but the speed v is NOT constant. When r is large the planet moves slowly and when r is small it moves fast, so the product that gives the swept area stays the same while v itself keeps changing. Do not confuse constant areal velocity with constant linear speed.
Yes. A circle is just a special ellipse where both foci meet at the centre. In a circular orbit r is fixed, so v is also constant, and the planet sweeps equal areas in equal times automatically. The Law of Areas holds for every orbit; the elliptical case is only where the speed change becomes obvious.
At perihelion, the point nearest the Sun. There r is smallest, so v is largest (from L = m·r·v), which makes KE = (1/2)mv² largest. At aphelion (farthest point) v is smallest, so KE is smallest. This is a very common NEET question - remember: nearest = fastest = maximum KE.
The kinetic energies of a planet in an elliptical orbit about the Sun at positions A, B and C are K_A, K_B and K_C. AC is the major axis and SB is perpendicular to AC at the Sun S (A is the nearest point/perihelion, C is the farthest point/aphelion). Then:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The line joining the Sun and a planet sweeps out equal areas in equal intervals of time, meaning the areal velocity dA/dt stays constant throughout the orbit.
dA/dt = L/2m, where L is the planet's angular momentum about the Sun and m is its mass. Since L is conserved for a central force, dA/dt is constant.
Because gravity is a central force that always points along the line joining the planet to the Sun. This gives zero torque about the Sun, and zero torque means angular momentum L stays constant.
Fastest at perihelion (nearest point to the Sun) and slowest at aphelion (farthest point). This follows directly from m·r·v = constant.
It links three ideas often tested together - orbital speed, angular momentum, and kinetic/potential energy in an elliptical orbit. NEET regularly asks to compare KE or speed at different orbit positions, which this law answers instantly.
