What is the primary force responsible for orbital motion?

The primary force responsible for orbital motion is the gravitational force between the orbiting body and the central body. According to Newton's Law of Universal Gravitation, this attractive force acts as the centripetal force, continuously pulling the orbiting object towards the center of its path and preventing it from flying off into space due to its inertia. Without gravity, stable orbits would not be possible.

Why doesn't a satellite fall to Earth if gravity is constantly pulling it?

A satellite doesn't fall to Earth because it's moving horizontally at a very high speed, known as orbital velocity. While gravity continuously pulls it downwards, the Earth's surface curves away beneath it at the same rate the satellite 'falls'. This creates a continuous state of freefall around the Earth, resulting in a stable orbit rather than a crash. It's essentially 'missing' the Earth as it falls.

What is the difference between orbital velocity and escape velocity?

Orbital velocity is the specific speed an object needs to maintain a stable, closed orbit around a central body at a given distance. Escape velocity, on the other hand, is the minimum speed an object needs to completely break free from the gravitational pull of a celestial body and never return. Escape velocity is always $sqrt{2}$ times the orbital velocity at the same radial distance from the center of the planet.

Why is the total mechanical energy of an orbiting satellite negative?

The total mechanical energy of an orbiting satellite is negative because it is 'bound' to the central body. This negative value indicates that energy must be supplied to the satellite to allow it to escape the gravitational field and move to an infinite distance, where its potential and total energy would be zero. If the total energy were positive, the satellite would escape the orbit; if it were zero, it would just barely escape.

What are geostationary satellites and why are they important?

Geostationary satellites are artificial satellites that orbit Earth in the equatorial plane with an orbital period exactly equal to Earth's rotational period (24 hours). This makes them appear stationary from the ground. They are crucial for global communication (television, internet, telephone), weather forecasting, and navigation, as they provide continuous coverage to a specific region on Earth.

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Orbital Motion

Physics

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Version 1Updated 22 Mar 2026

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Orbital motion describes the curved path, or trajectory, that an object takes around another object due to the influence of a central force, most commonly gravity. This phenomenon is a direct consequence of Newton's Law of Universal Gravitation, where the attractive force between two masses provides the necessary centripetal force to keep the orbiting body in its path. For stable orbits, the gravi…

Quick Summary

Orbital motion describes the path an object takes around another due to gravity. The gravitational force acts as the centripetal force, keeping the object in its curved trajectory. Key parameters include orbital velocity ( $v_o = sqrt{GM/r}$ ), which is independent of the orbiting mass and decreases with increasing radius.

The time period of orbit ( $T = 2pi sqrt{r^3/GM}$ ) follows Kepler's Third Law, where $T^2 propto r^3$ . An orbiting satellite possesses kinetic energy ( $K = GMm/2r$ ) and gravitational potential energy ( $U = -GMm/r$ ).

Its total mechanical energy ( $E = -GMm/2r$ ) is negative, indicating it is gravitationally bound. Geostationary satellites are a specific type, orbiting at a fixed altitude ( $35,786,\text{km}$ above Earth's surface) with a 24-hour period, crucial for communication.

The sensation of 'weightlessness' in orbit is due to continuous freefall, not an absence of gravity.

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Key Concepts

Derivation of Orbital Velocity

The orbital velocity is derived by equating the gravitational force acting on the satellite to the…

Relationship between Orbital Radius and Time Period (Kepler's 3rd Law)

Kepler's Third Law is a direct consequence of the orbital velocity derivation. Since $v_o = \frac{2pi r}{T}$ …

Total Energy of a Satellite and Binding Energy

The total mechanical energy ( $E$ ) of a satellite in orbit is the sum of its kinetic energy ( $K$ ) and…

Orbital Velocity: —

v_o = \sqrt{\frac{GM}{r}}

(independent of satellite mass

m

)

Time Period: —

T = \frac{2\pi r}{v_o} = 2\pi \sqrt{\frac{r^3}{GM}}

(Kepler's 3rd Law:

T^2 \propto r^3

)

Kinetic Energy: —

K = \frac{1}{2}mv_o^2 = \frac{GMm}{2r}

Potential Energy: —

U = -\frac{GMm}{r}

Total Energy: —

E = K + U = -\frac{GMm}{2r}

Binding Energy: —

-E = \frac{GMm}{2r}

Relationship: —

K = -E

U = 2E

Orbital Radius: —

r = R_E + h

(where

R_E

is Earth's radius,

h

is altitude)

Geostationary Satellite: —

T = 24,\text{hours}

, orbits in equatorial plane,

h \approx 35,786,\text{km}

Weightlessness: — Due to continuous freefall, not absence of gravity.

Escape Velocity: —

v_e = \sqrt{2} v_o = \sqrt{\frac{2GM}{r}}

VET KUTE

Velocity:

v_o = \sqrt{GM/r}

Escape:

v_e = \sqrt{2} v_o

Time Period:

T^2 \propto r^3

Kinetic Energy:

K = -E

U — Potential Energy:

U = 2E

Total Energy:

E = -GMm/2r

(always negative)

Equatorial (for Geostationary)

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