Problem 31 - A Complete Resource Book in Physics for JEE Main

Question

Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth, This is because, (A) the solar cells and batteries in satellites run out. (B) the laws of gravitation predict a trajectory spiralling inwards. (C) of viscous forces causing the speed of satellite and hence height to gradually decrease. (D) of collisions with other satellites.

Step-by-Step Solution

Answer

The correct reason why satellites have a finite life and sometimes their debris falls back to Earth is due to viscous forces causing the speed of the satellite and its height to gradually decrease, leading to orbital decay and re-entry into Earth's atmosphere. Thus, the best answer is (C).

Step 1: Option A - Solar cells and batteries run out

While it is true that the solar cells and batteries in satellites can deteriorate, leading to reduced performance or complete failure, the exhaustion of these power sources is not directly related to the reason why satellites fall back to Earth. Therefore, this answer is not the best option.

Step 2: Option B - Gravitational laws predict a spiraling inward trajectory

The laws of gravitation do dictate the motion of satellites in orbit, but they do not typically predict a trajectory spiraling inwards without any external factors. Orbits are generally maintained in a delicate balance between gravitational and centrifugal forces. If there were no external factors present, a stable orbit could theoretically be maintained indefinitely. Thus, this option is not the most appropriate answer.

Step 3: Option C - Viscous forces decrease satellite speed and height

Satellites in orbit around the Earth do experience some level of viscous forces due to the thin atmosphere at high altitudes. These forces can cause the satellites to gradually lose altitude and speed. As the satellite loses altitude, it experiences increased atmospheric drag, which continues to decrease its speed and height. This process is known as orbital decay and ultimately results in the satellite re-entering Earth's atmosphere, causing the debris to fall back to Earth. Thus, this option is the correct answer.

Step 4: Option D - Collisions with other satellites

Although collisions with other satellites or space debris can occur, they are relatively rare events. While such incidents may lead to damage or even the destruction of a satellite, they are not the primary reason why satellites have finite lifetimes and their debris falls back to Earth. Hence, this option is not the best answer. Based on the analysis above, the option that most accurately explains why satellites have finite life and debris sometimes falls to Earth is: (C) Viscous forces causing the speed of satellite and hence height to gradually decrease.