Orbital Velocity Formula with solved numerical problem

Spread the love

Here in this post, we will list down different forms of the Orbital velocity formula or equation. We will present here 3 sets of formula 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 Set1:


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 Set2:

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 Set3: [ for near-orbit satellite]


(2 expressions for Near Orbit)

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

Formula sets (Graphical Representation)

orbital velocity derivation

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)
rE =6.38×106 m (Earth’s radius)
mE =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 +rE =2.25×105 m + 6.38×106 m = 6.61×106 m

So, Orbital speed.
V = √[(G mE)/r] = [G mE)/r ]1/2  = 7.76 x 103 m/s

Related Posts for you

Derivation of the above-listed formula

Definition

Orbital Velocity Formula with solved numerical problem

Spread the love
Scroll to top
error: physicsTeacher.in