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.
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