As observed from earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from earth, this would

The correct answer is: not be true because the major gravitational force on mercury is due to sun.

Let's understand the physical reasoning step-by-step:

1. Observation of the Sun from Earth:
The Earth orbits the Sun in a nearly circular (slightly elliptical) orbit under the gravitational pull of the Sun. From the frame of reference of the Earth, the Sun appears to revolve around the Earth in a similar circular path. This is a simple relative motion of a two-body system (Earth and Sun) where the Earth's motion is primarily governed by the Sun's gravity.

2. Motion of Mercury:
Unlike the Sun, Mercury does not orbit the Earth, nor is its motion primarily governed by the Earth. The gravitational force between any two bodies of masses $m_1$ and $m_2$ separated by a distance $r$ is given by Newton's law of gravitation:
$F=\frac{G{m}_1{m}_2}{r^2}$
Because the mass of the Sun is extremely large compared to the Earth, the major gravitational force acting on Mercury is due to the Sun. As a result, Mercury revolves around the Sun in its own orbit with a much shorter orbital period and higher speed than the Earth.

3. Relative Motion of Mercury as observed from Earth:
Since both the Earth and Mercury are independently orbiting the Sun at different speeds and distances, the motion of Mercury relative to the Earth is a combination of both of their motions. As observed from the Earth, Mercury's path in the sky is not a simple circle. Instead, it exhibits complex, non-circular motion, including periods of apparent retrograde motion (where it appears to temporarily reverse its direction in the sky). Thus, the statement is not true for Mercury because its motion is primarily governed by the Sun's gravity, not the Earth's.