radius of satellite orbit

Question

the equation of radius of satellite orbit R_o= p/1+e cosθ.        p= h²/µ

p=semi latus rectum

h=magnitude of drbital momentum of a satellite

µ= GM_e

 G =gravitational constant

 M_e=mass of the earth

  e =eccentricity

 

Answer 1

Hi, Rudraraju K.

To find the radius of a satellite orbit Ro, follow these steps:

1. Identify Given Parameters
2. p = (h^2) / μ (semi-latus rectum)
3. e = eccentricity of the orbit
4. θ = true anomaly, angle from perigee
5. μ = G * Me (standard gravitational parameter)
6. h = specific angular momentum of the satellite
7. Apply the Orbital Radius Equation
8. Use the given equation for the orbital radius:
9. Ro = p / (1 + e * cosθ)
10. where p = (h^2) / μ
11. Substitute p into the Equation
12. Ro = [(h^2) / μ] / (1 + e * cosθ)
13. Simplify the Expression
14. Ro = (h^2) / [μ * (1 + e * cosθ)]
15. Final Computation
16. Plug in numerical values for h, μ, e, and θ.
17. Compute the denominator (1 + e * cosθ).
18. Divide h^2 by the computed denominator multiplied by μ.
19. The result gives the satellite’s orbital radius Ro at a given true anomaly θ.