Which of the following methods has led to the earliest discoveries of massive planets orbiting near their parent stars a. detecting a planet ejected from a binary star system b. detecting the starlight reflected off the planet c. detecting the gravitational effect of an orbiting planet (the wobble"") by looking for the doppler shifts in the star's spectrum d. detecting the infrared light emitted by the planet

c. detecting the gravitational effect of an orbiting planet (The Wobble"") by looking for the Doppler shifts in the star's spectrum

Explanation:

In a solar system the mass of the star and planets affect each other's orbital  movements. The center of gravity of a star and a planet is inside the star. This causes the star to be closer and farther from the Earth at different times. Due to this wobble the star appears to be red shifted when it is farther and blue shifted when it is closer.

When the mass of the planet is high, like a hot Jupiter it causes more wobble i.e., change in radial velocity. This makes it easier to detect the planet. The earliest hot Jupiter found by this method is the planet 51 Pegasi b.

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.