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jupiter is the most massive planet in

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our solar system

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and due to its proximity to the

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terrestrial planets it accepts a

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relatively large gravitational force on

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these inner planets

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jupiter essentially pushes and pulls

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them out of their ideal circular orbits

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and in this study we explore the

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influence of jupiter on the orbital

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dynamics of the earth

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and the implications for our planets

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spin dynamics and climate variability

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this is directly relevant to

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exoplanetary science as we discover more

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and more planets

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in multiplanetary systems with

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potentially habitable planets

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there has been a long lasting debate on

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whether it is beneficial for a planet in

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the habitable zone to have a giant's

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companion or not

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in terms of making that planet more or

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less a habitable

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for instance in the 1980s it was

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proposed that

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a giant planet could act as a shield and

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protect inner planets from harmful

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impacts

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but later on dynamic simulation showed

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that the impact rate could actually

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increase because jupiter jupiter

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destabilizes smaller objects out of

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their orbit

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and could actually shoot them towards

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the earth

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additionally impacts are not always

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harmful but can also carry essential

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volatiles to terrestrial

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planets that are necessary for habitable

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conditions

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so as we weighty advantages against the

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disadvantages

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of having a giant companion we should

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really consider also another important

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implications of the presence of a giant

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planet

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gravitational impact on the smaller

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planets and how it can alter their

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orbits and

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indirectly also their spin dynamics

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so currently for the earth jupiter

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drives quasi-periodic cycles in the

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elapticity or the eccentricity of the

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earth

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100

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000 kilo years long and modulated by a

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400 kilo year cycle as can be seen in

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the bottom panel

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for the earth the orbit remains

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relatively circular and the amplitude of

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the eccentricity cycles

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is small this means that the variability

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in the total amount of annual global

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mean insulation varies only

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slightly but yet these slight changes

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are sufficiently large to drive drastic

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changes in global climate

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for instance the glacial interglacial

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cycles of the last million years

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are paced at eccentricity cycles

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if you look closely enough you'll also

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see that earth's orbital inclination

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changes

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and this doesn't affect the amount of

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insulation that the earth receives on a

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global annual mean scale

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but it does impact the tilt of the earth

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relative to the sun

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which means that the distribution of the

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so you can imagine that if jupiter would

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have been on a slightly different orbit

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the orbital cycles of earth and

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consequently also the insulation

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patterns of our planet would be

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different

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so what does this mean in for in terms

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of the climate cycles and habitability

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on earth

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to answer these questions i use an

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ensemble of alternative solar system

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and body simulations and in these

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simulations that are ran by

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our collaborator john t horner the

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initial position of jupiter varies

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between

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3.2 au and 7.2 au

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the initial eccentricity of jupiter

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varies systematically between 0 and 0.4

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not all of these systems are stable some

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of them are dynamically

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unstable for instance when a planet

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collides with the sun

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with another planet or is ejected out of

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the system completely

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so the lifetime of each of those

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individual simulations are indicated in

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the figure

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the eccentricity of jupiter is indicated

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by the

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y-axis whereas the semi-major axis of

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jupiter is indicated by the x-axis

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overall simulations where jupiter has a

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low eccentricity

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they are dynamically more stable than

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when jupiter would have had a high

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eccentricity

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the red circle indicated here indicates

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our current solar system configuration

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and will be indicated in the next few

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figures as well that have the same

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outline

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so let's take a look at some of the

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results um in these figures the black

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regions indicate

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unstable simulations some of these

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regions for instance around 4.5 au

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and 6 au these are regions where saturn

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and jupiter

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are in resonance which allows for a much

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wider range of stable configurations

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there are also regions of instability

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for instance if jupiter would have been

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slightly more inward at 5 a.u

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the solar system would have been become

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dynamically unstable

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in this figure on the left we are now

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showing the maximum eccentricity that

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earth's orbit reaches

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uh for all the stable dynamical

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simulations

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in general the pattern that emerges is

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that when jupiter's eccentricity

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increases

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secondly when jupiter would be

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positioned more closely

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inwards and the rate at which earth's

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eccentricity changes

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would change as well so as jupiter would

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have been moving

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closer inwards the orbital cycles have a

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shorter duration

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currently earth's decentralized has a

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period of around 100 kilo years

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with jupiter at 3.2 au the main period

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would decrease up to

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since the annual global mean amount of

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insulation that the earth receives is

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directly a function of eccentricity

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we can calculate the maximum change in

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insulation so for a modern earth

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insulation varies

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but by roughly 0.5 watts per square

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meter

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between an eccentricity maxima and

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minimum and this has been

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driving great climatic fluctuations like

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the glacial interglacial cycles

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so in some of our simulations that we

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record here

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the difference in insulation can

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sometimes reach two or sometimes even

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five watts per square meter

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so you can imagine this could have

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massive implications for

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the climate variability on the earth's

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surface

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we can do exactly the same analysis for

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the orbital inclination

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and we find that if we change

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jupiter's orbit it doesn't majorly

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influence the maximum

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change in the orbital inclination

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however

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if we change jupiter's semi-major axis

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and move jupiter closer inwards it does

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impact

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the rate of change at which the

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inclination is changing

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so jupiter closer inward results in more

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rapid cycles in the orbital inclination

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and in terms of habitability we would

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like to investigate whether more rapid

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cycles

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or would improve the inhabitable

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habitable conditions or not

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but the orbital parameters are only part

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of the story

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and the spin motions of a planet play an

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important role for the climate

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modulation and are directly affected by

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changes in eccentricity and orbital

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inclination

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because the earth is not a rigid body it

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produces an equatorial bulge as a result

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of its really fast rotation

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and because the moon and the sun are not

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exactly aligned with the earth's equator

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where the bulge is forming they

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essentially try to pull the bulge

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towards the ecliptic which drives a

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processional motion of the earth's axis

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the orbital inclination has a direct

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influence on the earth's actual tilt

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or the oblique so what i do is i apply

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an obliquity model to the output of the

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ant body simulations to calculate how

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oblique and precession change over time

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um here i'm showing the output of the

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obliquity model for

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precession on the left and for obliquity

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on the right

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um and i'm using um them on

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previous simulations that are most

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similar uh

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to earth's current earth so in blue i

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plot the historical values for

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precession and obliquity

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and in orange are the values that we

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calculate for the simulation more

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similar to

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our current solar system and you see the

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comparison between the two figures shows

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that the model is working properly and

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it validates our method

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so this obliquity model was applied to

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all the stable alternative solar system

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simulations

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for obliquity on the left it becomes

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evident that as we move jupiter closer

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inwards

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it results in much longer obliquity

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cycles

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the rate at which earth's axis precesses

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is not so much dependent on the

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semi-major axis or the

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eccentricity of jupiter but rather by

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the planetary architecture of the

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alternative solar system and the

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resonances within it

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now we find this interesting feature

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that when jupiter is closer inwards the

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eccentricity cycles that determine the

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total amount of insulation are

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relatively short

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while the obliquity cycles that control

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the distribution of the

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insulation are relatively long and this

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can have some interesting climatic

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consequences

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as various climate feedbacks act on

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different time skills

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uh for instance what would happen to the

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surface climate if the eccentricity

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cycles are

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as short as thirty 000 year

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would we just experience really rapid

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glacial interglacial cycles or would the

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rate of change be

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too high for ice caps to grow and cover

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large surfaces

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so what would happen to atmospheric

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dynamics or ocean circulations that are

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also important climate controllers

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we took a first step at trying to

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simulate the change in climate evolution

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across a one million year time interval

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and use a simple energy moisture balance

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model that is coupled to a dynamic 3d

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ocean model and a sea ice model

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while applying also time varying

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astronomical forcing so the figure shown

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here shows the simulation most

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comparable to our modern solar system

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earth's eccentricity cycles are roughly

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100 kilo years long

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and vary between zero and 0.5 obliquity

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cycles are roughly 40 kilo years long

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we find that as we simulate the sea ice

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variability

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seasonal sea ice varies with mainly

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eccentricity

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whereas the year round sea ice varies

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the figure here shows a simulation where

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the planetary architecture is very

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different

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jupiter is much closer inwards earth's

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eccentricity cycles are 30 kilo years

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long

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and very very small amplitude whereas

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the obliquity cycles are roughly

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30 000 kilo years long and very

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drastically between 20 and 30 degrees

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in this case the seasonal sea ice varies

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with the obliquity

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and the year-round sea ice is only

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present when the obliquity is low enough

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to sustain sea ice throughout the summer

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months

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the surface climate dynamics between the

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two configurations are

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just very very different and i should

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also note that the model used here is

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relatively simple and many of the

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climate feedbacks are

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not included for instance we do not

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simulate land-based eyes

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which can have very different dynamics

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to see

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sea ice also the response times is

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different than that of sea ice

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so in future work we do aim to use a

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more complex climate model that also

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uses a dynamic atmosphere so we can

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account for

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changing wind patterns and cloud

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so i will leave the conclusions up here

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but i do want to emphasize

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that as we find more planets in the

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habitable zone in multiplanetary systems

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we should not ignore the long-term

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orbital evolution as we assess a

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planet's habitability