MAE 161A HW2 (3)
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School
University of California, Los Angeles *
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Course
161A
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
Pages
4
Uploaded by PrivateCapybaraPerson2168
MAE
161A
Homework
#
2
Use
this
page
as
your
coversheet
Name:
SID:
Honor
Code
Statement:
I,
the
undersigned,
in
accordance
with
the
UCLA
Student
Conduct
Code, hereby
affirm
that
the
work
that
I
have
presented
on
this
assignment
is
my
own
and only
my
own,
and
that
I
have
not
copied
work
of
other
students."
Signature:
(To
be
submitted
via
Gradescope)
l.
Kepler’s
Equation.
a.
Determine
the
eccentricity
of
an
elliptical
orbit
that
spends
%
of
its
orbit
between
0
=90°
and
0
=270°.
b.
Find
the
distance
to
perigee
for
a
geocentric
satellite
that
satisfies
(a)
with
a
period
of
12
hours.
2.
A
satellite
1s
1n
an
elliptical
orbit
around
the
earth.
At
perigee,
the
satellite
1s
at
600
km
altitude
and
moving
9.0
km/s.
a.
Complete
the
following
table
Semi-major
axis
Magnitude
of
Eccentricity
Distance
to
apogee
Orbital
period
b.
Using
Kepler's
Equation,
determine
the
time,
Tso,
for
the
satellite
to
move
from
perigee
to
a
true
anomaly
of
6
=80°.
2.
A
satellite
1s
1n
an
elliptical
orbit
around
the
earth.
At
perigee,
the
satellite
1s
at
600
km
altitude
and
moving
9.0
km/s.
a.
Complete
the
following
table
Semi-major
axis
Magnitude
of
Eccentricity
Distance
to
apogee
Orbital
period
b.
Using
Kepler's
Equation,
determine
the
time,
Tso,
for
the
satellite
to
move
from
perigee
to
a
true
anomaly
of
6
=80°.
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3.
Hyperbolic
Kepler’s
Equation.
Voyager
|
recently
became
the
only
man-made
object
to
leave
the
solar
system.
Its
current
speed
is
v=17.2
km/s
and
its
distance
from
the
sun
is
r=18.8
x
10
km.
Assume
the
perihelion
of
its
orbit
is
located
at
the
orbital
radius
of
the
Jupiter,
~SAU=7.48
X
108
km.
(Hint
find
eccentricity
and
orbital
parameter
first)
a.
Suppose
Voyager
coasted
to
its
current
position
from
perihelion,
find
the
turn
angle
of
its
orbit
about
the
sun.
b.
How
long
did
it
take
to
get
to
its
current
location
from
Jupiter’s
orbital
radius?