Problem 78 - Master Resource Book in JEE Main Physics

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

(c) of viscous forces causing the speed of satellite and hence height to gradually decrease

Step 1: Understanding Satellite Life Limits

Satellites have a finite operational life due to the depletion of resources like solar cells and battery life. Over time, these components degrade, leading to the satellite becoming non-functional.

Step 2: Analyzing Gravitational Effects

The laws of gravitation—specifically Newton's law of universal gravitation—maintain the satellite's orbit. However, these alone do not predict a natural inward spiral of the orbit unless influenced by external factors.

Step 3: Examining Viscous Forces

Viscous forces, such as atmospheric drag, affect objects at lower altitudes. These forces reduce the speed of the satellite, leading to a decrease in its orbital height and eventual re-entry into the Earth's atmosphere.

Step 4: Considering Collisions

Collisions with other satellites or space debris can alter the trajectory of a satellite. However, this is not the primary reason for the gradual decrease in height over time for most satellites.

Key Concepts

Gravitational Effects on Satellites

Gravitational forces play a crucial role in maintaining a satellite's orbit around the Earth. This force is governed by Newton's law of universal gravitation. According to this law, every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. For satellites, this translates to a gravitational pull that keeps them in orbit.

Without this gravitational force, satellites would drift off into space instead of following a circular or elliptical path around the Earth. It's important to understand that while gravity is essential for maintaining an orbit, it does not naturally cause an inward spiral. A satellite's trajectory would remain stable if not affected by other forces or influences.

• Newton's law ensures the satellite stays in a predictable path.
• Gravitational pull alone does not result in orbital decay.

Viscous Forces and Atmospheric Drag

Viscous forces, particularly atmospheric drag, are significant factors that impact a satellite's lifespan, especially those in lower Earth orbits. This drag occurs because even at high altitudes, there are still traces of Earth's atmosphere that exert a force on the satellite as it moves through it.

Atmospheric drag reduces the satellite's speed, causing a gradual loss of altitude. As the speed decreases, the satellite's orbit deteriorates and eventually leads to re-entry into the atmosphere, where it may burn up due to frictional heat.

• Lower Earth orbit satellites are more susceptible to atmospheric drag.
• The drag can result in a shorter operational period for satellites.

This is why many satellites are designed to operate at higher altitudes, where the atmosphere is thinner and exerts less drag force.

Satellite Collisions

Satellite collisions, while less common than other factors, are still a risk to consider in space operations. As the number of satellites and space debris increases, so does the likelihood of collisions. These collisions can have serious consequences, such as crippling a satellite's ability to function properly or changing its orbit.

When a collision occurs, the resulting debris can pose further threats to other operational satellites, creating a cascading effect known as the Kessler syndrome. This effect describes a scenario where collisions lead to more space debris, increasing the chances of additional collisions.

• Collisions can severely damage satellites, ending their lifecycle prematurely.
• Space debris generated from collisions increases risks for other satellites.

While not the primary reason for orbital decay, the impact of collisions is significant enough that satellite operators must take preventive measures to avoid such scenarios as much as possible.