4. (Inspired by recent eclipse...) If a small body were to orbit a much larger stationary body (e.g. a star), its motion would be governed by the following ODEs: x = GMs(xs-x) [(x-xs)²+(y-ys)2] 3/2 x(0) = xo x(0) = xo GMs (ys-y) ÿ = [(x-xs)²+(y-ys)2]3/2 y(0) = Yo y(0) = yo Where x(t) and y(t) give the position of the small body over time, G is the gravitational constant, Ms is the mass of the large body, and xs and y, specify its fixed position. a) Convert this problem to a system of first order ODEs. b) Assume G = = = 10, Ms 5, xsys = 0 with initial conditions xo == -1, yo = 0, xo = 5, yo = 5 and use ode45 to solve the system until t = 3. You can use the attached code and complete the missing parts. Also include the final plot of the trajectory.
4. (Inspired by recent eclipse...) If a small body were to orbit a much larger stationary body (e.g. a star), its motion would be governed by the following ODEs: x = GMs(xs-x) [(x-xs)²+(y-ys)2] 3/2 x(0) = xo x(0) = xo GMs (ys-y) ÿ = [(x-xs)²+(y-ys)2]3/2 y(0) = Yo y(0) = yo Where x(t) and y(t) give the position of the small body over time, G is the gravitational constant, Ms is the mass of the large body, and xs and y, specify its fixed position. a) Convert this problem to a system of first order ODEs. b) Assume G = = = 10, Ms 5, xsys = 0 with initial conditions xo == -1, yo = 0, xo = 5, yo = 5 and use ode45 to solve the system until t = 3. You can use the attached code and complete the missing parts. Also include the final plot of the trajectory.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please solve a b
![4. (Inspired by recent eclipse...) If a small body were to orbit a much larger stationary body (e.g. a star), its
motion would be governed by the following ODEs:
x =
GMs(xs-x)
[(x-xs)²+(y-ys)2] 3/2
x(0) = xo
x(0) = xo
GMs (ys-y)
ÿ
=
[(x-xs)²+(y-ys)2]3/2
y(0) = Yo
y(0) = yo
Where x(t) and y(t) give the position of the small body over time, G is the gravitational constant, Ms is the
mass of the large body, and xs and y, specify its fixed position.
a) Convert this problem to a system of first order ODEs.
b) Assume G
=
=
=
10, Ms 5, xsys = 0 with initial conditions xo
==
-1, yo = 0,
xo = 5, yo = 5 and use ode45 to solve the system until t = 3. You can use the attached code and complete
the missing parts. Also include the final plot of the trajectory.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b248bcb-d422-475d-9311-e6ae6a3d6b31%2Faf663ff8-8227-4b46-b334-5cfb61343066%2Fn6i1dt_processed.png&w=3840&q=75)
Transcribed Image Text:4. (Inspired by recent eclipse...) If a small body were to orbit a much larger stationary body (e.g. a star), its
motion would be governed by the following ODEs:
x =
GMs(xs-x)
[(x-xs)²+(y-ys)2] 3/2
x(0) = xo
x(0) = xo
GMs (ys-y)
ÿ
=
[(x-xs)²+(y-ys)2]3/2
y(0) = Yo
y(0) = yo
Where x(t) and y(t) give the position of the small body over time, G is the gravitational constant, Ms is the
mass of the large body, and xs and y, specify its fixed position.
a) Convert this problem to a system of first order ODEs.
b) Assume G
=
=
=
10, Ms 5, xsys = 0 with initial conditions xo
==
-1, yo = 0,
xo = 5, yo = 5 and use ode45 to solve the system until t = 3. You can use the attached code and complete
the missing parts. Also include the final plot of the trajectory.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)