What is Orbital Velocity in Physics? | Definition, Derivation, Formulas – Gravitation

Orbital Velocity Definition Physics:
1. Orbital velocity of a satellite is the minimum velocity required to put the satellite into a given orbit around earth.

2. Orbital velocity is the velocity needed to achieve balance between gravity’s pull on the satellite and the inertia of the satellite’s motion. The satellite’s tendency to keep going. This is approximately 17,000 mph (27,359 kph) at an altitude of 150 miles (242 kilometers).

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What is Orbital Velocity in Physics? | Definition, Derivation, Formulas – Gravitation

Orbital Velocity of Satellite Formula:
Orbital velocity of a satellite is given by

\(v_{o}=\sqrt{\frac{G M}{r}}=R \sqrt{\frac{g}{R+h}}\)

M = mass of the planet
R = radius of the planet
h = height of the satellite from planet’s surface.

If a small satellite is revolving near the earth’s surface, then r = (R + h) ≈ R.
Now, orbital velocity,

v0 = \(\sqrt{g R}\) = 7.92 km/h

If v is the speed of a satellite in its orbit and v0 is the required orbital velocity to move in the orbit, then

(i) If v < v0, then satellite will move on a parabolic path and satellite will fall back to earth.
(ii) If v = v0, then satellite will revolve in circular path/orbit around earth.
(iii) If v0 < v < ve, then satellite will revolve around earth in elliptical orbit.

  • The orbital velocity of jupiter is less than the orbital velocity of earth.
  • For a satellite orbiting near earth’s surface

(a) Orbital velocity = 8 km/s
(b) Time period = 84 min approximately
(c) Angular speed, ω = \(\frac{2 \pi}{84}\)rad/min = 0.00125 rad/s

Energy of a Satellite in Orbit:
Total energy of a satellite, E = KE + PE

= \(\frac{G M m}{2 r}+\left(-\frac{G M m}{r}\right)=-\frac{G M m}{2 r}\)

Time Period of Revolution of Satellite:
The time taken by a satellite to complete one revolution around the earth, is known as time period of revolution of satellite.
The period of revolution (T) is given by

T = \(\frac{2 \pi r}{\sqrt{\frac{G M}{r}}}=\frac{2 \pi(R+h)}{v_{0}}\)

Height of Satellite:
As it is known that the time period of satellite,

T = \(2 \pi \sqrt{\frac{r^{3}}{G M}}=2 \pi \sqrt{\frac{(R+h)^{3}}{g R^{2}}}\) ……(i)

By squaring on both sides of Eq. (i), we get

T² = 4π²\(\frac{(R+h)^{3}}{g R^{2}}\)
⇒ \(\frac{g R^{2} T^{2}}{4 \pi^{2}}\) = (R + h)3
⇒ h = \(\left(\frac{T^{2} g R^{2}}{4 \pi^{2}}\right)^{1 / 3}\) – R

By knowing the value of time period, the height of the satellite from the earth surface can be calculated.

Binding Energy of Satellite Definition:
The energy required by a satellite to leave its orbit around the earth (planet) and escape to infinity is called binding energy of the satellite. Binding energy of the satellite of mass m is given by

Binding Energy Formula:

BE = + \(\frac{G M m}{2 r}\)

Have you ever thought, when we throw a ball above the ground level, why it returns back to the ground. It’s because of gravity. When a ball is thrown above the ground in the opposite direction, a gravitational force acts on it which pulls it downwards and makes it fall. This phenomena is called gravitation.

Learn relation between gravitational field and potential field, Kepler’s law of planetary, weightlessness of objects in absence of gravitation, etc.

Newton’s Law of Gravitation Central Force
Acceleration Due to Gravity Factors Affecting Acceleration Due to Gravity
Gravitational Field Intensity Gravitational Potential Energy
Relation between Gravitational Field and Potential Kepler s Laws of Planetary Motion
Earth’s Satellite Orbital Velocity
Escape Velocity Weightlessness