Problem 32 - A Complete Resource Book in Physics for JEE Main

Question

Both the earth and the moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon (A) will be elliptical. (B) will not be strictly elliptical because the total gravitational force on it is not central. (C) is not elliptical but will necessarily be a closed curve. (D) deviates considerably from being elliptical due to influence of planets other than the earth.

Step-by-Step Solution

Answer

The correct answer is (B) The Moon's orbit will not be strictly elliptical because the total gravitational force on it is not central, as the Moon is influenced by both Earth's and the Sun's gravity, causing its orbit to deviate from a perfect ellipse.

Step 1: Understanding gravitational forces acting on the Moon

First, let's consider the gravitational forces acting on the Moon. There are two primary sources of gravitational forces: Earth's gravitational force and the Sun's gravitational force. Earth's gravitational force is the main force that keeps the Moon in orbit around Earth, whereas the Sun's gravitational force acts on the Moon and Earth as a whole.

Step 2: Analyzing the Moon's orbit

Since both Earth and the Moon are under the influence of the Sun's gravity, the Moon's orbit around Earth is affected by the Sun's gravitational force. As a result, the Moon's orbit may not be a perfect ellipse but might still possess some elliptical characteristics.

Step 3: Considering the influence of planets other than Earth

The Moon's orbit can be affected by the gravitational pull of other planets in our Solar System. However, the gravitational effects of these planets are relatively minor compared to the gravitational forces exerted by Earth and the Sun. Now, let's examine the given answer choices and select the most accurate one. (A) The Moon's orbit will be elliptical - This statement is partially true, but the Sun's gravitational force might cause the Moon's orbit to deviate from a perfect ellipse. (B) The Moon's orbit will not be strictly elliptical because the total gravitational force on it is not central - This statement is true since the Moon is influenced by both Earth's and the Sun's gravity, causing the Moon's orbit to not be a perfect ellipse. (C) The Moon's orbit is not elliptical but will necessarily be a closed curve - This statement is not accurate; the Moon's orbit has some elliptical characteristics, but it might not be strictly elliptical. (D) The Moon's orbit deviates considerably from being elliptical due to the influence of planets other than Earth - This statement is not true because the effect of other planets on the Moon's orbit is relatively minor compared to Earth and the Sun's gravitational forces. Based on our analysis, the correct answer is: (B) The Moon's orbit will not be strictly elliptical because the total gravitational force on it is not central.