Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is b

NCERT Exemplar · Q4

Q. 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.

(d) of collisions with other satellites.

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Concept understanding — Gravitational Potential Energy

Gravitational Potential Energy

The Intuition: Energy Stored by Height

Imagine holding a heavy book above the floor. Your arm feels tired — that's because you're working against gravity. If you let go, the book falls and gains speed. Where did that motion come from? It came from the position of the book. By lifting it, you stored energy in the Earth–book system. That stored energy is gravitational potential energy.

The higher you lift, the more energy you store. The heavier the object, the more energy you store. This is the core idea: Gravitational potential energy is the energy an object has because of its position in a gravitational field.

The Precise Definition

Gravitational potential energy ( $U$ ) is the work done against gravity to bring an object from a reference point (usually the ground) to its current position.

For objects near the Earth's surface (where gravity is roughly constant), the formula is beautifully simple:

U = mgh

Where:

$U$ = gravitational potential energy (joules, J)
$m$ = mass of the object (kg)
$g$ = acceleration due to gravity (≈ 9.8 m/s² on Earth)
$h$ = height above the reference point (m)

Why "Potential"?

The word "potential" means "stored and ready to be used." The book at height $h$ has the potential to do work — it can smash a table, compress a spring, or generate sound when it hits the ground. That energy was put in when you lifted it.

The Reference Point is Arbitrary

Here's a crucial point: Only changes in gravitational potential energy matter. You can choose any height as $h = 0$ . In most problems, we take the ground as zero, but you could take the floor, the tabletop, or even the ceiling.

If you lift a 2 kg book from the floor ( $h = 0$ ) to a shelf ( $h = 2$ m), the change in potential energy is:

\Delta U = mg\Delta h = 2 \times 9.8 \times 2 = 39.2 \text{ J}

If you instead took the shelf as $h = 0$ , the book on the floor would have negative potential energy ( $-39.2$ J). The difference between the two positions is still 39.2 J — that's what matters.

Watch out

Never say "the object has $mgh$ energy" without specifying the reference level. The value is meaningless without a zero point.

The Bigger Picture: Variable Gravity

The formula $U = mgh$ works only when $g$ is constant — that is, near Earth's surface. For large distances (like a rocket leaving Earth), gravity weakens with distance. The general formula for gravitational potential energy between two masses $M$ and $m$ separated by distance $r$ is:

U = -\frac{GMm}{r}

The negative sign means that potential energy is zero at infinite separation and becomes more negative as objects come closer. This is the true definition, and $U = mgh$ is a special case of it (derived by approximating near the surface).

Key Takeaways for Exams

Gravitational potential energy is always relative — you must state or imply a reference level. …

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The key idea is that even in the near-vacuum of space, a satellite experiences a tiny but persistent drag force from the residual atmosphere. This viscous force reduces its speed, causing it to lose altitude and eventually re-enter the Earth's atmosphere.

The question asks why satellites have finite lives and why their debris eventually falls to Earth. Many students instinctively think of power failure or collisions, but the real culprit is much subtler — and it's a beautiful example of how even negligible forces, given enough time, can produce dramatic effects.

Let's examine each option carefully.

Option (A): Solar cells and batteries running out.

This would indeed stop the satellite from functioning — it would become a dead piece of metal. But a dead satellite doesn't automatically fall to Earth. It would continue orbiting just as a rock or any inert object does. Power failure explains why a satellite stops working, not why it descends. So this is incorrect.
Option (B): Laws of gravitation predicting a spiralling trajectory.

This is a common misconception. In a pure two-body problem (Earth + satellite), with no other forces, the orbit is a perfect ellipse (or circle) that repeats forever. Gravitation alone never causes an orbit to spiral inward — that would violate conservation of energy and angular momentum. So this is false.
Option (C): Viscous forces causing speed and height to gradually decrease.

This is the correct physical explanation. Even at orbital altitudes (say 200–1000 km), there is a very thin atmosphere — not a perfect vacuum. The satellite experiences a tiny drag force (a viscous force) from collisions with air molecules. …

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Q.Satellites orbiting the earth have finite life and sometimes debris of satellites fall to the earth. This is because,

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