Question

Problem: Trip to the moon

You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the earth with enough speed to make it to the moon. Some information that will help during this problem:

m_{earth} = 5.9742 x 10^{24} kg

r_{earth} = 6.3781 x 10^{6} m

m_{moon} = 7.36 x 10^{22} kg

r_{moon} = 1.7374 x 10^{6} m

d_{earth to moon} = 3.844 x 10^{8} m (center to
center)

G = 6.67428 x 10^{-11} N-m^{2}/kg^{2}

1)On your first attempt you leave the surface of the earth at v = 5534 m/s. How far from the center of the earth will you get?

2)Since that is not far enough, you consult a friend who
calculates (correctly) the minimum speed needed as v_{min}
= 11068 m/s. If you leave the surface of the earth at this speed,
how fast will you be moving at the surface of the moon? Hint
carefully write out an expression for the potential and kinetic
energy of the ship on the surface of earth, and on the surface of
moon. Be sure to include the gravitational potential energy of the
earth even when the ship is at the surface of the moon!

3)Which of the following would change the minimum velocity needed to make it to the moon?

Please include the process!

Answer #1

mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to center)
G = 6.67428 x 10-11 N-m2/kg2
103 kg satellite is orbitting the earth in a circular orbit with
an altitude of 1500 km.
1) How much energy does it take just to get it to this
altitude?
2) How much kinetic energy does it have...

mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to
center)
G = 6.67428 x 10-11 N-m2/kg2
A 1200 kg satellite is orbitting the earth in a circular orbit
with an altitude of 1600 km.
1)
How much energy does it take just to get it to this
altitude?
2)
How much kinetic energy does it...

mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to
center)
G = 6.67428 x 10-11 N-m2/kg2
A 1900 kg satellite is orbitting the earth in a circular orbit
with an altitude of 1400 km.
1)
How much energy does it take just to get it to this
altitude?
J
2)
How much kinetic energy does...

When a mass is far away from the moon it has a speed 3.2 times
its escape velocity from the moon. With what speed in metres per
second must the object have be launched from the surface of the
moon? (Mmoon = 7.36 X 1022 kg;
Rmoon = 1.74 X 106 kg)
The answer is 7970 m/s. Consider initial and final energy
conditions

In
this problem, you will calculate the location of the center of mass
for the Earth-Moon system, and then you will calculate the center
of mass of the Earth-Moon-Sun system. The mass of the Moon is
7.35×1022 kg
k
g
, the
mass of the Earth is 6.00×1024 kg
k
g
, and
the mass of the sun is 2.00×1030 kg
k
g
. The
distance between the Moon and the Earth is 3.80×105 km
k
m
. The
distance...

You Will need
Radius of the Moon = 1.74 x 106 m
Lunar Module Mass 5.56 x 103 kg
G = 6.67 x 10-11 Nm2 / kg2
4. In Apollo's lunar program, the command module orbits the
Moon, while the lunar module lands on the surface of the Moon. The
command module's orbit was circular and was 110 km above the Moon's
surface. The speed of the orbit was uniform and lasted 2.00 hours.
Determine the centripetal force on the...

QUESTION 1
Part 1
Engineers wish to launch a satellite from the surface of the
Moon. What is the minimum speed the satellite must have to escape
the Moon’s gravity – that is, what is the escape velocity at the
surface of the Moon? The Moon has a mass of 7.3x10^22 kg and a
radius of 1.7x10^6 m.
a.
1700 m/s
b.
5.7x10^6 m/s
c.
It depends on the mass of the satellite.
d.
2400 m/s
Part 2
The satellite...

Problem: Orbital Mechanics
A spaceship is waiting for launch at the Kennedy Space Center
(Located at Latitude 28.52o North of the Equator) . The spaceship
has a mass of m = 2000 kg.
a) What is the gravitational potential energy the spaceship has
sitting and waiting for launch.
b) What is the kinetic energy the spaceship has sitting and
waiting (calculate K relative to the center of the earth).
c) The spaceship is attached to rockets that are going to...

1.Zero, a hypothetical planet, has a mass of 4.9 x 1023 kg, a
radius of 3.3 x 106 m, and no atmosphere. A 10 kg space probe is to
be launched vertically from its surface. (a) If the probe is
launched with an initial kinetic energy of 5.0 x 107 J, what will
be its kinetic energy when it is 4.0 x 106 m from the center of
Zero? (b) If the probe is to achieve a maximum distance of...

What is the minimum speed with which a meteor strikes the top of
Earth’s stratosphere (about 41.5 km above the surface), assuming
that the meteor begins as a bit of interplanetary debris far from
Earth and stationary relative to Earth? Assume that the drag force
is negligible until the meteor reaches the stratosphere. Mass of
Earth is 5.974 × 1024 kg; radius of Earth is 6.371 × 106 km; and
gravitational constant is 6.674 × 10−11 N·m2/kg2.
b. The tension...

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