Physics · Gravitation · NEET
No. In a circular orbit the speed is constant, so KE is constant. But an elliptical orbit has different Sun-planet distances, so the speed changes. KE is highest at perihelion (closest point) and lowest at aphelion (farthest point). Only in a perfect circle would KE stay constant.
KE is maximum at perihelion, the point nearest the Sun. KE is minimum at aphelion, the point farthest from the Sun. This is because the planet is fastest when it is closest to the Sun and slowest when it is farthest.
Because angular momentum L = m·v·r is conserved (gravity is a central force, so it applies no torque about the Sun). L stays constant, so when r decreases the speed v must increase. Smaller r means bigger v, which means bigger KE = (1/2)mv².
Two things stay constant: total mechanical energy E = KE + PE, and angular momentum L. As the planet nears the Sun its PE becomes more negative (it drops into a deeper well), so KE rises to keep E fixed. As it moves away, KE falls and PE rises. The trade-off keeps E constant.
Rank the points only by their distance from the Sun. The closest point has the largest KE, the farthest has the smallest. Do not rank by distance along the path or by which point 'looks' higher — only Sun-to-planet distance matters.
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) and C is the farthest (aphelion). Then:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
KE = (1/2)mv², where m is the planet's mass and v is its orbital speed at that point. Since v changes along an ellipse, KE also changes.
At perihelion, the point closest to the Sun. This follows from angular momentum conservation: m·v·r is constant, so smaller r gives larger v.
No. Gravity always points from the planet toward the Sun (a central force), so it exerts zero torque about the Sun. Angular momentum L stays constant throughout the orbit.
Negative. Any bound orbit (closed ellipse or circle) has total energy E = KE + PE that is negative. The negative sign means the planet is trapped by the Sun's gravity and cannot escape.
They are the same idea seen two ways. Kepler's second law (equal areas in equal times) is a direct result of angular momentum conservation. That same conservation makes the planet fast near the Sun (high KE) and slow far away (low KE).
