Spacecraft Motion and Re-entry

This assignment delves into the physics behind spacecraft movement, including the application of Newton's Law of Universal Gravitation to satellite orbits. It examines key concepts like gravitational force, centripetal force, and the optimal re-entry angle for a manned spacecraft. The text also highlights the complexities of atmospheric re-entry, emphasizing the need for heat shielding due to friction and the importance of achieving the correct trajectory for a safe landing.

PHYSICS
Name
Subject
Tutor
Date

Compare qualitatively low Earth and geostationary orbits
A low Earth orbit technically refers to any satellite that is less than 1500km in altitude and is
usually approximately 300km from the Earth's surface. Low Earth Orbits have their orbital
periods that last for about 960 minutes with each orbital velocity being approximately 8km/s. on
the other hand, geostationary orbits, due to their orbital period of 24 hours, usually remain at a
fixed position on the surface of the Earth1.
They are relatively higher than the Low Earth Orbits in altitude with their altitude about
36000km but with a lower orbital velocity of about 3km/s. a geostationary orbit is considered as
a special geo-synchronous orbit type. A geosynchronous orbit is any orbit that has an orbital
period of 24 hours. It should, however, be noted that not all geo-synchronous orbits are geo-
stationery since geo-stationary orbits must be equatorial i.e. traveling directly above the equator.
In a nutshell, low Earth orbits have lower altitudes than geostationary; have higher orbital
velocity and shorter orbital periods.
Account for the orbital decay of satellites in low earth orbit
A satellite in a stable orbit around the Earth is found to be encompassing some amount of
mechanical energy which is a combination of both its gravitational energy that is due to its
altitude and kinetic energy resulting from its high speed of motion. This means the lower the
altitude of the orbit of a satellite the lower the mechanical energy it contains.
1 Bate, Roger R. Fundamentals of Astrodynamics. New York: Courier Corporation, 2010.
Curtis, Howard D. Orbital Mechanics: For Engineering Students. London: Butterworth-
Heinemann, 2015.

In the process of motion, satellites encounter frictional forces with the sparse outer fringes
contained in the atmosphere. This friction culminates into the loss of energy thereby making the
satellites no longer viable hence the satellite drops to a new altitude that corresponds to the
resultant energy after energy losses due to friction. At the new level, the satellite tends to move
at a higher speed than before even though there is additional kinetic energy that is extracted from
the potential energy that was lost. It should be recalled that the lower the orbits, the higher the
velocities of the orbits2.
The process of orbital decay is a cyclic one as the new lower orbits of the satellites are found to
be in relatively denser atmosphere thereby leading to even further friction thus energy loss. The
process is a continuous one and the speed increases with time.
Identify data sources, gather, analyze and present information on the contribution of one of
the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard,
Esnault-Pelterie, O'Neill or von Braun
Konstantin Tsiolkovsky, who was a Russian scientist, came up with numerous ideas which were
perceived to prophetic and very significant in space travel even though he was not making direct
contributions to space travel at the time he lived. Among the key principles and ideas that he
came up with included rocket propulsion, the use of liquid fuels not forgetting multi-stage
2 Davies, E. Brian. Why Beliefs Matter: Reflections on the Nature of Science. Chicago:
Oxford University Press, 2010.

rockets. Konstantin Tsiolkovsky illustrated the application of Newton’s 3rd law of motion and the
law of conservation of linear momentum would be applicable in rocket3.
This is the principle that underlies the functioning of rockets and was important in understanding
their operations. Secondly, Konstantin Tsiolkovsky came up with the idea that liquid oxygen
and liquid hydrogen could be used as rocket fuels in such a way that the thrust released by the
rocket could be varied. These very fuels were deployed in the Saturn V rocket that was used in
the powering of the Apollo missions to the moon and the application of liquid fuels was proved
to be important in manned spaceflight as they are able to allow the control of g-forces that are
experienced by astronauts unlike in the use of solid fuels.
Identify why the term 'g-forces' is used to explain the forces acting on an astronaut during
launch
‘G-Forces’ are the forces that an astronaut experiences in terms of the gravitational strength of
the Earth on the surface of the Earth. The force experienced by an astronaut while on the surface
of the Earth is equivalent to 1G: w=mg where g=9.8 N/kg. Taking an example of a rocket which
is accelerating upwards at 9.8m/s2 then it would be mean the astronaut would experience 2Gs net
force which is twice the force it experienced due to the gravity of the Earth. An astronaut would
experience 0Gs when in a free-fall. The term g-forces are normally used since it is easy to relate
3 Leondes, C. T. Advances in Control Systems: Theory and Applications. Chicago:
Elsevier, 2014.
Lissauer, Jack J. Fundamental Planetary Science: Physics, Chemistry, and Habitability. Paris:
Cambridge University Press, 2013.

to and that it eases calculations in regard to the forces which can be withstood by the human
body during launch.
Discuss issues associated with safe re-entry into Earth's atmosphere and landing on the
Earth's surface
As a result of the high temperatures and velocities experienced, re-entry becomes a complex
procedure as well as the fine balance of the trajectory that is needed to safely land. In order to
successfully land a space vehicle, the initial step is to slow down and then travel back down via
the atmosphere, processes that have to occur simultaneously with the drag of the atmosphere
hence slowing the vehicle as it descends4. Friction is created as a result of the high velocity of the
vehicle thereby heating it up to more than 3000⁰C in relation to the flow of air. This leads to the
need for a resistant shielding of very high temperature in most cases carbon or ceramic based is
used as these can withstand such temperature thereby protecting the vehicle while in the
descending process.
Identify that there is an optimum angle for safe re-entry for a manned spacecraft into
Earth's atmosphere and the consequence of failing to achieve this angle
The optimum angle required for safe re-entry into the atmosphere lies between 5.2⁰ and 7.2⁰.
Any angle beyond this range would culminate into the upward friction become very great hence
4 Lowrie, William. Fundamentals of Geophysics. Paris: Cambridge University Press,
2015.
Quarles, Billy. Three Body Dynamics and Its Applications to Exoplanets. Chicago: Springer,
2017.

decelerating the craft at a very high speed thereby causing the craft to burn up and melt. A re-
entry angle less than the provided range would make the aircraft bounce off the atmosphere
making it return to space. In such a situation, the craft may not be having enough fuel to allow it
make a second attempt thereby burning up5.
Discuss the importance of Newton's law of universal gravitation in understanding and
calculating the motion of satellites
 The velocity of the orbit must be known in order to launch a satellite. The centripetal
force on to which a body is subjected to must be equivalent to the force exerted by
gravity on the same body in the orbit.
 Newton’s Law of Universal Gravitation is important in the comprehension and
calculation of the motion of satellites since the law is needed in the quantification of the
value of Fg used in derivation the velocity of the orbits.
 Newton's Law is also used in the derivation of Kepler's Law of Periods, an important tool
in the extensive understanding of the motion of orbits.
5 Rainey, Larry B. Space Modeling, and Simulation: Roles and Applications Throughout
the System Life Cycle. Manchester: AIAA, 2014.

References
Bate, Roger R. Fundamentals of Astrodynamics. New York: Courier Corporation, 2010.
Curtis, Howard D. Orbital Mechanics: For Engineering Students. London: Butterworth-
Heinemann, 2015.
Davies, E. Brian. Why Beliefs Matter: Reflections on the Nature of Science. Chicago: Oxford
University Press, 2010.
Leondes, C. T. Advances in Control Systems: Theory and Applications. Chicago: Elsevier, 2014.
Lissauer, Jack J. Fundamental Planetary Science: Physics, Chemistry, and Habitability. Paris:
Cambridge University Press, 2013.
Lowrie, William. Fundamentals of Geophysics. Paris: Cambridge University Press, 2015.
Quarles, Billy. Three Body Dynamics and Its Applications to Exoplanets. Chicago: Springer,
2017.
Rainey, Larry B. Space Modeling, and Simulation: Roles and Applications Throughout the
System Life Cycle. Manchester: AIAA, 2014.
Stevens, Brian L. Aircraft Control, and Simulation. Manchester: John Wiley & Sons, 2016.
Warren, Neville G. Excel HSC Physics. New York: Pascal Press, 2013.