SampleFinalProblems
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School
Townsend Harris High School *
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Course
1234
Subject
Geography
Date
Nov 24, 2024
Type
Pages
4
Uploaded by sn338454
1.
A satellite is launched into Earth orbit from Cape Canaveral (latitude 28.4
N) such that at burnout
the altitude is
z
= 650 km, the velocity is
V
= 9.0 km/s, and the flight path angle is
= +10º.
For
Earth
= 398,600 km
3
/s
2
and
r
earth
= 6378 km.
a)
What is the eccentricity of the orbit,
e
?
e =
b)
What is the true anomaly at burnout,
bo
(degrees)?
bo
=
2.
An earth satellite is launched into an orbit with the following orbital elements:
i
= 20º
a
= 13,000 km
= 30º
= 315º
e
= 0.5
What will be the minimum
scalar
V
(km/s) needed to change this orbit into an equatorial orbit?
This
V
is accomplished by a single, impulsive maneuver.
Hint: it may be helpful to draw a
careful
sketch
of this orbit, showing the inclination, location of perigee, etc.
V = _____________
km/s
equatorial
plane
?
?
?
̂
3.
A solar research mission is designed to use Mercury to change the velocity of a spacecraft so that it
attains its perihelion as close to the sun as possible.
The spacecraft arrives at Mercury on a
Hohmann transfer from Earth.
The radius of Mercury is
r
= 2487 km, and Mercury has no
atmosphere.
a) Since the heliocentric velocity vector of the spacecraft is to be deflected
towards
the sun, on
which side (sunlit or dark) should the flyby of Mercury occur?
b) What is the value of
V
(relative to Mercury)
of the spacecraft when it arrives at Mercury’s SOI?
Does the spacecraft “overtake” the planet, or the planet, the spacecraft?
c) What is the maximum possible magnitude of velocity change,
V
, that the flyby can theoretically
accomplish?
d) By what angle
is the spacecraft’s flight path deflected with respect to
Mercury
for this
V
?
e) By what angle is the spacecraft’s flight path deflected with respect to the
Sun
?
f) The mass of the spacecraft is
m
= 1000 kg.
What is the
magnitude
of the linear momentum
change experienced by Mercury as a result of the flyby (kg-m/s)?
Useful data:
Radius of orbit (km)
Orbital speed (km/s)
(km
3
/s
2
)
Earth
1.496
10
8
29.78
3.986
10
5
Mercury
5.79
10
7
47.87
2.232
10
4
Sun
-
-
1.327
10
11
\
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4.
At time
t
= 0, ignition of a rocket on a launch pad on the
moon
occurs.
Due to a malfunction, the
thrust is equal to only 75% of the initial weight of the rocket.
The mass flow rate,
𝑚̇
, is constant.
Determine the time
t
at which lift-off finally occurs, expressing your answer in terms of
I
sp
and
other appropriate constants (
not
𝑚̇
).
t =
Have a wonderful and blessed Christmas/Holiday break
…
and make sure to wear those
“heavy boots!”