Question

Distance planet travels in an orbit. This tool is provided by a third party. Though your activity may be recorded, a page refresh may be needed to fill the banner. 0/2 371902.2070904.qx3zqy7 Distance planet travels in an orbit Consider a planet that follows an elliptical orbit. The perimeter of an ellipse with a major axis a and minor axis b is 4a ²√1-k²sin²0 do Va²b² where k = For a given a major axis a and minor axis b, calculate the distance the planet travels, by completing: a 1. the subfunction TrapzPlanet that uses trapeziodal numerical integration (using the internal function trapz) and a given number of discrete points. 2. the subfunction IntegratePlanet that uses the internal function integral. Ex: a = 3.01*10^9; b = 2.74*10^9; [trapzApprox, numIntegrate] = Planet Distance (a, b, 1000) produces trapzApprox = 1.8074e+10 numIntegrate = 1.8074e+10 Function > Save C Reset MATLAB Documentation 1 function [trapzApprox, numIntegrate] = PlanetDistance (a, b, points) 2 trapzApprox=TrapzPlanet (a, b, points); 3 numIntegrate=IntegratePlanet (a,b); 4 end 5 6 function trapzApprox=TrapzPlanet (a, b, points) 8 % Your code goes here 9 k=sqrt (a^2-b^2)/a; theta=linspace(0, pi/2, points); f=sqrt (1-k^2* (sin(theta)).^2); 10 11 12 end

Answer 1

To calculate the distance traveled by a planet in an elliptical orbit, we can use trapezoidal numerical integration or the 'integral' function in MATLAB. These methods allow us to approximate the distance based on the major axis and minor axis of the ellipse representing the orbit.

Step-by-step explanation:

Calculation of the Distance Traveled by a Planet in an Elliptical Orbit

Given the major axis (a) and minor axis (b) of the ellipse representing the planet's orbit, we can use numerical integration techniques to calculate the distance traveled by the planet.

1. Trapezoidal Numerical Integration

We can approximate the distance traveled using the trapezoidal rule, which divides the area under the curve into trapezoids and sums their areas. The formula is:

Distance = TrapzPlanet(a, b, points)

where a is the major axis, b is the minor axis, and points is the number of discrete points used in the calculation.

2. Integration using MATLAB's 'integral' Function

We can also use the 'integral' function in MATLAB to perform numerical integration and obtain a more accurate result for the distance traveled.

Distance = IntegratePlanet(a, b)