Can you solve this in MATLAB? We want to have a one to one transformation between Keplerian
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Can you solve this in MATLAB?
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We want to have a one to one transformation between Keplerian orbital elements and cartesian coordinates that can be used in a broad set of problem. Therefore, the objective of this problem is to write a series of subroutines as a toolbox for future problems. To that end, write the following subroutines as Matlab functions or equiva- lent (each subroutine must be in a different file and copied into the final report): a) Transformation from cartesian coordinates to Keplerian orbital elements. This has to be done as a function script in the form (a,ecc,inc,raan,argp,f) = cart2orb(x,y,z,vx,vy, vz) whose inputs are the cartesian coordinates x, y, and z with their respective velocities vx, vy, (expressed in km and km/s respectively), and whose outputs are the semi-major axis (a) (in km), the eccentricity (ecc), the inclination (inc), the right ascension of the ascending node (raan), the argument of perigee (argp), and the true anomaly (f) (with all the angles expressed in degrees). Use = 398600.4418 km/s as the gravitational constant of the Earth. b) Transformation from Keplerian orbital elements to cartesian coordinates. Similar to the previous problem, write a function script in the form (x,y,z,vx,vy, vz) = orb2cart(a,ecc.inc,raan,argp,f). c) Transformation from mean anomaly to true anomaly. Write a Matlab function in the form f = kepler (M,ecc) that is able to obtain the approxi- mate value of the true anomaly (f) of an orbiting object around the Earth from the information of mean anomaly (M) and eccentricity (ecc) of the orbit. We want to have a one to one transformation between Keplerian orbital elements and cartesian coordinates that can be used in a broad set of problem. Therefore, the objective of this problem is to write a series of subroutines as a toolbox for future problems. To that end, write the following subroutines as Matlab functions or equiva- lent (each subroutine must be in a different file and copied into the final report): a) Transformation from cartesian coordinates to Keplerian orbital elements. This has to be done as a function script in the form (a,ecc,inc,raan,argp,f) = cart2orb(x,y,z,vx,vy, vz) whose inputs are the cartesian coordinates x, y, and z with their respective velocities vx, vy, (expressed in km and km/s respectively), and whose outputs are the semi-major axis (a) (in km), the eccentricity (ecc), the inclination (inc), the right ascension of the ascending node (raan), the argument of perigee (argp), and the true anomaly (f) (with all the angles expressed in degrees). Use = 398600.4418 km/s as the gravitational constant of the Earth. b) Transformation from Keplerian orbital elements to cartesian coordinates. Similar to the previous problem, write a function script in the form (x,y,z,vx,vy, vz) = orb2cart(a,ecc.inc,raan,argp,f). c) Transformation from mean anomaly to true anomaly. Write a Matlab function in the form f = kepler (M,ecc) that is able to obtain the approxi- mate value of the true anomaly (f) of an orbiting object around the Earth from the information of mean anomaly (M) and eccentricity (ecc) of the orbit.
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Related Book For
Statistical Reasoning for Everyday Life
ISBN: 978-0321817624
4th edition
Authors: Jeff Bennett, Bill Briggs, Mario F. Triola
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