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Astronomy 1 > Dynamical Astronomy > Flashcards

Dynamical Astronomy Flashcards

1
Q

one-body systems

A

systems with two masses, where
one is significantly larger than the other.

only the lighter body moves significantly

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2
Q

Kepler’s 1st Law

A

The orbit of each planet is an ellipse with the Sun at one focus

(centre of mass of the system at the focus but sun is much more massive than planets)

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3
Q

Kepler’s 2nd Law

A

For any planet, the line connecting the planet to the Sun
sweeps out an equal area in an equal time

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4
Q

Kepler’s 3rd Law

A

The cubes of the semi-major axes of the planetary orbits are proportional to the squares of the planet’s orbital periods

a^3/T^2=constant

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5
Q

Newton’s 1st law

A

Every body continues in its state of rest or uniform motion in a
straight line until acted on by an external force

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6
Q

Newton’s 2nd law

A

The rate of change of momentum of a body is proportional to
the applied force, and is in the direction of the force

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7
Q

Newton’s 3rd Law

A

To every action, there is an equal and opposite reaction

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8
Q

a planet moving in a circular orbit must…

A

be feeling a force and must be accelerating

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9
Q

proving kepler 3

A

using centripetal acceleration and gravity

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10
Q

natural units for the solar system

A

au and sidereal years

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11
Q

geostationary

A

if a satellite orbits Earth in the equatorial plane with a period of 1 sidereal day

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12
Q

calculating orbital radius

A

using Newton’s second law and universal law of gravitation

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13
Q

Conservation of angular momentum in elliptical orbits

A

It is conserved in orbits because the force of gravity acts along the line joining
the masses, so cannot exert a torque on them.

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14
Q

how is angular momentum changed?

A

twisting forces (torque)

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15
Q

why is L=mva for circular motion

A

sin(pi/2)=1

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16
Q

eccentricity e=0

A

circle

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17
Q

eccentricity e= close to 1

A

long,thin orbit

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18
Q

eccentricity e=1

A

parabola (not a closed orbit)

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19
Q

eccentricity e>1

A

hyperbola

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20
Q

relating the parameter in an ellipse

A

AC+BC=constant

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21
Q

perihelion

A

point in orbit when closest to the sun
rp=a-ae

22
Q

aphelion

A

point in orbit when furthest from the sun
ra=a+ae

23
Q

name of perihelion and aphelion for orbits around earth

A

perigee and apogee

24
Q

name of perihelion and aphelion for orbits around stars

A

periastron and apastron

25
Q

name of perihelion and aphelion for orbits in general

A

periapsis and apoapsis

26
Q

how to equate angular momentum at A and P

A

using Kepler’s second law

L=mva(a+ae)=mvp(a-ae)

which rearranges to
vp/va=1+e/1-e

27
Q

how to find speed of circular orbit

A

equation gravitational force with centripetal force

28
Q

case 1 - kick in the direction of motion

A

speed of mass increases
new orbit is elliptical
radius of old orbit becomes periastron of new orbit

29
Q

case 2 - kick in the opposite direction to motion

A

speed of mass decreases
new orbit is elliptical
radius of old orbit becomes apastron of the new orbit

30
Q

case 3 - radial kicks perpendicular to direction of motion

A

no torque applied so no change in angular momentum
velocity does not change
radius of old orbit becomes semilatus rectum of new orbit

31
Q

radial kicks always…

A

increase kinetic energy

32
Q

conserved quantities for two stars orbiting common centre of mass

A

linear momentum m1v1=m2v2
velocities have opposite directions

angular momentum
Ltotal=m1r1v1sinθ1+m2r2v2sinθ2

33
Q

conservation of energy - total energy of a planet or satellite

A

kinetic energy and gravitational potential energy

34
Q

gravitational potential energy

A

the minus the work done to separate two masses to an infinite distance apart

35
Q

derivation of gravitational potential energy

A

first consider work done for small change in distance
integrate with limits of r and infinity

36
Q

total energy for one-body orbits

A

Etotal=1/2mv^2-Gm1m2/r

37
Q

escape velocity

A

if E>0 then the mass escapes the gravitational attraction
the speed at which it just escapes is the escape velocity

38
Q

polar coordinates radial vector

A

r defined from the focus

39
Q

polar coordinates true anomaly

A

theta, defined from the periapsis side of the major axis to r

40
Q

most fuel effecient method of changing orbit

A

Hohmann transfer orbit

41
Q

stage 1 Hohmann transfer orbit

A

boost speed to inject into transfer orbit (velocity required at perigee)

42
Q

Hohmann transfer orbit intermission

A

wait until it reaches exit point, the apogee point of the orbit in half a period

43
Q

stage 2 Hohmann transfer orbit

A

need to change velocity again to enter GEO

44
Q

Are Hohmann transfers effective?

A

minimises fuel required (just two small burns)
not designed to minimise trip time

45
Q

aerobraking

A

make elliptical orbit more circular
Mar’s thin atmosphere is a source of friction which reduces periapsis speed. This reduces semi-major axis and eccentricity

46
Q

how does a gravity assist work?

A

spacecraft approaches stationary planet at a speed > escape velocity.

Trajectory of the spacecraft is deflected into a hyperbolic orbit

accelerates as it is attracted to planet the decelerates as it flies away

47
Q

gravity assist - where does the extra momentum and energy come from?

A

actually slows down the planet (change infinitesimal)

48
Q

deriving for the two body problem

A

centre of mass remains stationary

use normal gravitational force and sub in m1r1=m2r2 for r2 and define a mass

49
Q

two-body problem

A

two masses always sit on same line passing through centre of mass

trace out same ellipse, one just larger

eccentricities same

50
Q

changing equations for 2-body systems

A

M=m1+m2
a=a1+a2
v=v1+v2

Astronomy 1 (6 decks)

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