Download Answer to Question 3

Answer to Question Number 1
(a)
Planetary orbits are ellipses with the Sun at one focus.
(1)
Semi-major axis; Half the maximum diameter of the ellipse
(1)
Eccentricity; The separation of the foci divided by the major axis
(1)
Perihelion; The point in an object’s orbit closest to the Sun.
(1)
Aphelion; The point in an object’s orbit furthest from the Sun.
(1)
Siderial period: The time for a planet to go round the Sun with respect to the distant
stars.
(1)
Synodic period: The time between equivalent alignments with respect to Earth.
(1)
(b)
Hohmann transfer orbits are orbits requiring the least energy (in the form of
propellant) to reach the orbit of one planet from another. They are elliptical, with (for
orbits to Mars) the perihelion at Earth and aphelion at Mars.
(2)
An Earth-Mars Hohmann transfer orbit has a major axis of 2.5 AU (semi-major axis,
1.25 AU). Using Kepler’s 3rd Law, the period is therefore
1.253 = 1.4 years. Since
we will only use half the orbit to reach Mars, the time from launch to arrival will be
0.7 years (about 8½ months).
(3)
Such a spacecraft cannot be launched at any time, as Earth and Mars need to be in the
correct alignment at launch to ensure the spacecraft arrives at the orbit of Mars at the
same point as Mars itself.
(2)
(c)
For a mission to Neptune, Hohmann transfer orbits require a large amount of
propellant (even though they are the lowest energy orbits, a large velocity change at
launch is required) and still take a significant time. In this example, a mission to
Neptune on a Hohmann orbit would take (major axis = 30.1 AU)
15.553
= 30 years!
2
(3)
An alternative is to take advantage of other planets in a gravity assist trajectory,
where angular momentum is transferred from the planet to the spacecraft.
Significantly less propellant needs to be carried, making for an easier initial launch.
Further, higher speeds can be achieved through multiple passes of planets,
significantly reducing flight times. For example, Voyager 2, launched in 1977,
reached Neptune after only 12 years in 1989, having already made flybys of the other
Jovian planets picking up speed on the way.
(3)
Answer to Question Number 2
The terrestrial planets are the four planets in the inner Solar System (Mercury, Venus,
Earth and Mars). They all have rocky surfaces, high average densities (4-6000 kg m-3)
and differentiated cores (e.g., the Earth has an iron/nickel core, surrounded by a
silicate mantle with a thin rocky lithosphere). All have atmospheres to varying
degrees (Mercury, very tenuous, but the others, significant – e.g., Mars, about 6 mbar,
Earth 1000 mbar). The surface temperatures are all quite high (even Mars can reach
300 K at the equator at midday in summer).
(5)
The Jovian planets are much more massive than the terrestrial planets (the lightest,
Uranus is almost 15 times the mass of the Earth) and much larger (the smallest,
Neptune, is almost 4 times the Earth’s diameter). All are at much greater distances
from the Sun, and are correspondingly cooler. Their structure is significantly different
to the terrestrial planets. Current models suggest they comprise a thick (largely
hydrogen) atmosphere, a metallic hydrogen mantle and a comparatively small rocky
core. Temperatures are much lower and clouds tend to be of ammonia, methane and
similar compounds rather than of water. All have many natural satellites, many of
which may be regarded as small terrestrial planets in their own right (e.g., Europa,
Titan). Others are icy bodies with low average densities. By contrast, there are few
satellites amongst the terrestrial planets (the only one of significance is the Earth’s
moon) and all are rocky.
(5)
Venus has a dense carbon dioxide and sulphur dioxide atmosphere (~90 atm) and has
suffered a runaway greenhouse effect. The surface temperature is very high (~500 ºC)
in consequence, no liquid water can exist in this hostile environment.
Earth’s atmosphere (pressure, 1 atm) is primarily nitrogen (77%) and oxygen (21%)
the latter being a direct result of plant life breaking down carbon dioxide
(photosynthesis). With a much weaker greenhouse effect, and greater distance from
the Sun, an average temperature of 15 ºC means that water oceans (71% of the
surface), ice caps and water vapour clouds exist.
Mars has a much thinner (0.006 atm), mainly carbon dioxide, atmosphere. Coupled
with its distance from the Sun, the surface temperature rarely rises above 0 ºC and in
any case, the pressure is too low for liquid water to exist.
(5)
In the case of Venus, an early ocean would have quickly vapourised in the heat of the
Sun, and been dissociated by UV radiation from the Sun. Consequently, no water
would be left. Intense volcanic activity probably produced the dense, corrosive
atmosphere, producing the current conditions.
On Earth, the temperature did not rise high enough to vapourise the oceans, hence the
water was retained. Further, the appearance of life caused carbon dioxide to be locked
up in carbonate rocks, reducing the greenhouse effect and preventing a runaway
greenhouse as happened on Venus.
The surface of Mars shows dry river valleys, suggesting a much warmer and wetter
past. The lower mass of Mars resulted in the loss of the bulk of the atmosphere in two
ways: 1, lower gravity means the atmosphere could escape. 2, the lower mass meant
that the atmosphere was not replenished by volcanic outgassing and plate tectonics.
With reduced pressure, the temperature dropped, locking even more gas into polar
caps and (possibly) permafrost resulting in today’s dry, cold desert.
(5)
Currently the most successful method of detecting extrasolar planets is Doppler
spectroscopy of the parent star. This method exploits the gravitational tug on the parent
star by its orbiting planet(s), causing a periodic Doppler shift in the star’s spectrum. The
Doppler technique is most successful in detecting massive planets in close orbits as these
give large radial velocity shifts to the parent star. Indeed, most of the 50 or so planets
discovered fit these criteria. Other techniques include studying the light intensity from
stars to observe occultations (so far one positive success) and attempts to separate the
spectrum of reflected light from a planet’s surface from that of it’s parent star. The most
ambitious require space-based techniques such as optical interferometry to cancel the
star’s light, leaving the planets visible. This latter technique has the potential for
observing terrestrial planets.
(5)
The extrasolar planets detected to date are largely very different from those in our solar
system. In particular, many are high mass planets (typically several times the mass of
Jupiter) in very close orbits with periods of typically a few days. Others are in orbits with
greater eccentricity than any of the solar system planets. The high mass and closeness to
the star might suggest these are not gas giants, as these could not form in this region.
However, occultation studies indicate such “epistellar giants” have large radii and are
therefore “hot Jupiters”. The atmospheres of these planets may not be ammonia and other
volatile materials as on Jupiter, but rather alkali metal or silicate vapours.
A number of the planets discovered orbit within the “habitable zone” of their star. Whilst
liquid water cannot exist on a gas giant, it has been speculated that such planets may have
terrestrial world sized moons, just as Jupiter and Saturn do. The possibility therefore
exists for earth-like moons of these worlds.
(5)
Answer to Question 3
(a)
Solar panels use the photovoltaic effect in silicon or other semiconductors like
gallium arsenide. Typical power outputs are 1 A at 0.25 V for a 6 cm diameter silicon
cell at 1 AU from the Sun. For maximum efficiency, solar panels must be kept
aligned to the Sun and not allowed to overheat (hence high thermal conductivity
substrate materials must be used). Solar panels degrade by about 2% per year under
normal conditions, faster if subject to intense radiation from solar activity.
(2)
(b)
RTGs use heat from the decay of a radioactive isotope (usually Pu 238) to provide
power via the thermoelectric effect. They are efficient, compact and long lasting (the
RTGs on the Voyagers are still providing sufficient power after 20 years). There are
some safety issues, especially at launch, but RTGs are designed to survive intact in
case of accident. Further, the RTGs must be kept away from sensitive particle detection
or infra-red experiments to minimise their impact on these instruments. Decay rates are
similar to solar panels, about 2% per year.
(2)
(c)
Solar panels are suitable for use in the inner solar system as here there is sufficient
light for them to operate efficiently and there is no advantage in using RTGs. However,
beyond the orbit of Mars, solar panels become unfeasible due to the low light levels
and RTGs are therefore required. For example, if the same solar panels were used on
Cassini as on the Mars surveyor, they would only provide 800×(1.5/9/5) 2 = 20 W at
Saturn. Hence, panels over 40 times larger would be required.
(3)
(b)
Flyby/orbiter: Photographic surveys, spectroscopy, particle detection, plasmas and
magnetic and gravitational field studies (e.g., Galileo at Jupiter). Synthetic aperture
radar surface mapping (e.g., Magellan at Venus)
(2)
Atmospheric probe: Composition of atmosphere, atmospheric characteristics (pressure,
temperature etc.), meteorology (wind speeds), lightning and other electrical activity.
E.g., Galileo atmospheric probe, Huygens.
(2)
Landers: Surface imaging, composition (either by spectroscopy or direct chemical
sampling), long-term meteorology. E.g., Viking (Mars), Venera (Venus)
(2)
(c)
A schematic diagram of an ion engine is shown below:
+ve grid
Xe inlet
-ve grid
+ve ions
+ve ions
Hollow
accelerated
cathode
Electron
s
Magnetic field coils
Electron beam
Electrons produced in the hollow cathode impact on xenon atoms, ionising them. Xenon
is used as it is a heavy gas (mass ~131 au) hence a relatively high thrust can be achieved.
The electrons are confined by the magnetic field. The ions are accelerated between the
+ve and -ve grids, and are ejected into space with high velocity (~30 km/s). An electron
beam neutralises the ion beam, ensuring overall electrical neutrality of both the
spacecraft and the exhaust.
(5)
The thrust generated by an ion engine is quite small. For example, the engine on a
prototype spacecraft, DS1 provides a few grammes of thrust, compared with many
tonnes provided by a chemical engine. However, an ion engine can operate for many
months, compared to a few minutes for a chemical engine, hence large velocity changes
can be accomplished. The propellant requirement is also much lower, for example, DS1
initially carried about 80kg of Xe, orders of magnitude less than the chemical equivalent.
Hence, the advantages and disadvantages can be summed up as follows:
Advantages: Low mass, high specific thrust, sustainable, controllable.
Disadvantages: Low thrust, hence cannot be used, for example, to launch from a surface
or for an orbit insertion manoeuvre. Can only operate in a vacuum, hence cannot operate
in an atmosphere.
(5)