Question

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 push the ship into orbit. The goal is to give the ship enough kinetic energy to get it into low earth circular orbit. What is the gravitational potential energy of the low earth orbit? (400 km above the earth).

d) How much work must the rockets do on the spacecraft to get it into the low earth circular orbit (don’t forget to consider the kinetic energy it has in part b)?

e) In the low earth orbit, the spaceship docks with the International space station and picks up some supplies. They then depart to go repair a satellite in a geosynchronous orbit. What distance away is the geosynchronous orbit? (A geosynchronous orbit is a circular orbit where the object orbiting stays above the same spot on the earth as the earth rotates).

f) In order to make it to the new orbit, the spaceship fires its thrusters to increase its speed. It is a short and powerful burst, giving it a new speed while still at the low earth orbit. This new speed destroys the circular motion and the puts the craft into an elliptical orbit. This starting point becomes the orbit’s perigee. What speed is required to make the apogee of the orbit at the geosynchronous orbit distance? (Conservation of energy should tell you about the changes of the kinetic energy and potential energy required. Because gravity will not put any torque on the craft relative to the center of the orbit, use conservation of angular momentum to find the required speeds at the apogee and perigee.)

g) When the apogee has been reached, how must the speed be changed in order to establish a circular orbit?

Answer #1

A satellite of mass m = 2.00 ×103 kg is launched into a
circular orbit of orbital period T = 4.00 hours. Newton's
gravitational constant is G = 6.67 ×10−11 N∙m2/kg2, and
the mass and radius of the Earth are respectively M⨁ =
5.97 ×1024 kg and r⨁ = 6.37 ×106 m. Answer the following
questions.
What is the total mechanical energy (kinetic energy + potential
energy) of the satellite in orbit? Take the gravitational potential
energy of the satellite...

How much gravitational potential energy must a 3140-kg satellite
acquire in order to attain a geosynchronous orbit?
The answer to the above question is 1.67x10^11 J.
How much kinetic energy must it gain? Note that because of the
rotation of the Earth on its axis, the satellite had a velocity of
467 m/s relative to the center of the Earth just before launch.
Doing a 1/2mv^2 doesn't get the correct answer. The law of
conservation of energy would state that...

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:
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...

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...

In a shuttle craft of mass m = 3100 kg, Captain Janeway
orbits a planet of mass M = 8.50 ✕ 1025 kg, in
a circular orbit of radius r = 4.70 ✕ 107
m.
(a) What is the period of the orbit?
26887 s
(b) What is the speed of the shuttle craft?
10983 m/s
Janeway briefly fires a forward-pointing thruster, reducing her
speed by 1.70%.
(c) Just then, what is the speed of the shuttle craft?
10763 m/s...

It takes a delta launch vehicle 8 min to get to low earth orbit
about 100 miles up. If it went in a straight line (it doesn’t) and
its speed on orbit was 17,500 mph, how many g’s would the space
force service members go through? Ignore the rotation of the Earth
and just solve as the rocket is in one dimension. Convert all
values to metric and show the conversions.
2. The space force developed a new weapon system...

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...

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