Orbital Velocity Formula with solved numerical problem

Last updated on February 12th, 2022 at 03:08 pm

Here in this post, we will list down different forms of the Orbital velocity formula or equation. We will present here 3 sets of formulas including the near-orbit one. After this, we will also see how to use these formulas to solve numerical problems.

Orbital Velocity Formula – 3 sets of formulas are listed below:

Orbital Velocity Formula Set 1:

V = [(GM)/r]^1/2 ……………. (1)
( here G = gravitational Constant,
M is the mass of the central body i.e. for the formula of the orbital velocity of the earth’s satellite, M denotes the mass of the earth,
Here R = radius of the earth, h = height above the earth’s surface, And r = R +h )

Orbital Velocity Formula Set 2:

V = R . (g/r)^1/2 ……. (2)
(Here R = radius of the earth, h = height above the earth’s surface, And r = R +h )

Orbital Velocity Near Orbit equation Set 3: [ for near-orbit satellite]

(2 expressions for Near Orbit)

V = [(GM)/R]^1/2 ———–(3)
V_orbital =(gR)^1/2……….(4) here, R =radius of the earth

Formula sets (Graphical Representation)

Derivation of the above-listed formula

Sample Numerical problem based on Orbital velocity equation – with solution

Q) Assume that a satellite orbits Earth 225 km above its surface. Given that the mass of Earth is 5.97 x 10²⁴ kg and the radius of Earth is 6.38×10⁶ m, what is the satellite’s orbital speed?

Solution:
h =2.25×10⁵ m (height of the satellite’s orbit)
r_E =6.38×10⁶ m (Earth’s radius)
m_E =5.97×10²⁴ kg (Earth’s mass)
G = 6.67×10^-11 Nm^2/kg^2
Orbital velocity = V =?

We get the orbital radius r by adding the height of the satellite’s orbit to Earth’s radius.
r =h +r_E =2.25×10⁵ m + 6.38×10⁶ m = 6.61×10⁶ m