From RTN reference frame to ECI and orbital elements

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SUMMARY

This discussion addresses the conversion of position and velocity data from the RTN (Radial, Transverse, Normal) reference frame to ECI (Earth-Centered Inertial) coordinates and orbital elements for a chaser spacecraft relative to a target spacecraft. The target spacecraft's orbit is circular, with an altitude of 800,000 meters, while the chaser's RTN position is given as (30, 10, 10) meters and its mass is 1,000 kg. The user seeks to determine if it is feasible to derive the necessary ECI coordinates and orbital elements using the provided data, including the gravitational constant and Earth's radius.

PREREQUISITES
  • Understanding of RTN reference frame and its application in spacecraft dynamics
  • Knowledge of ECI coordinates and their significance in orbital mechanics
  • Familiarity with orbital elements and their calculation methods
  • Basic grasp of gravitational constants and their role in space navigation
NEXT STEPS
  • Research methods for transforming RTN coordinates to ECI coordinates
  • Learn about the calculation of orbital elements from position and velocity vectors
  • Study the implications of circular orbits on spacecraft dynamics and control
  • Explore simulation tools that can handle both RTN and ECI coordinate systems
USEFUL FOR

Aerospace engineers, spacecraft navigation specialists, and anyone involved in the simulation and control of spacecraft in relative motion will benefit from this discussion.

GNCstudent
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Hi all,
I'm curently meeting the following problem and can't figure it out by myself.
Assume we have to vehicles in space, a target and a chaser spacecraft . The target spacecraft defines the RTN frame of reference.
Given the position and velocity of the chaser in RTN-coordinates, how can I derive its representation in ECi coordinates and/or orbital elements ?
Is it even possible ?

The background of my problem is, that I'm using a controller, that only uses RTN coordinates. However, I'm trying to include another more commplex simulator as reference solution, that requires ECI coordinates as inital condition for the target and the relative difference coordinates in orbital elements from chaser to target.
I am aware that I need additional information, like the mass, the altitude, R_earth, mu and gravitational constant, which I could provide.
But is that enough?


A very first idea, was to assume, that the initial ECI-position of the target doesn't matter for the simple regulator. So I could just set them to a random value.. So the only thing that matters would be the distance expressed in orbital or ECI-coordinates from target to chaser. But I can't figure out , how to do that...
 
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Some data and simplifications, that can be used here :

- the target's orbit is circular
- the RTN position of the chaser is (30;10;10) m
- the mass of the chaser is 1000kg and the mass of the target is 8000kg
- the target has an altitude of 800e3 m
 
GNCstudent said:
Some data and simplifications, that can be used here :

- the target's orbit is circular
- the RTN position of the chaser is (30;10;10) m
- the mass of the chaser is 1000kg and the mass of the target is 8000kg
- the target has an altitude of 800e3 m
- Also the chaser has no initial velocity (it's zero)
 

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