1

•Kepler’s Laws

•P 2 = a3

•Newton’s Laws• Speed, velocity, acceleration, force, inertia, mass,

balanced and unbalanced forces

• F= ma

•Law of Universal Gravitation

2dMmGF =

Laws describing the planetary motion Weight and acceleration due to gravity1. Weight – gravitational force attracting an object to the Earth.2. How much is the weigh depends on how strong is the gravitational field of the planet

gmW

gsma

aRMG

amFR

MmGFW

Earth

grav

Earth

grav

Earth

Earth

=

==

=

=

==

2

2

2

/81.9

Acceleration due to gravity

Measured for objects in free fall

Calculating the mass of Earth

kg

GgRM

G

kmR

smgRMG

Earth

Earth

Earth

Earth

Earth

2411

2

2

2211

22

109.51067.6

81.9)10006378(

/kgm N1067.6

6378

/ 81.9

×=×

×=

==

⋅×=

=

==

−

−

Fundamental Astronomical constant

Newton’s version of Kepler’s 3rd empirical law:

Units: P - in seconds, a - in meters.

)(4 32

2

MmGaP+

=π

Allows to calculate masses

a

Mm

P

2

Gravitational Force

2dMmGF =

Week force:

G=6.67x10-11 Nm2/kg2

M=m = 1kgd= 1m

F= G=6.67x10-11 NM

aP

MmaP

MmGaP

32

32

322

79

)(79

)(4

=

+=

+=

π

M of Jupiter is much largerthan m of Satellite.

P in days instead of secondsa in meters

P in secondsa in meters

MaP

32 79= P in days

a in meters

Io

P= 1.77 daysa= 422 000 km kgM

PaM

27

2

3

109.1

79

×=

=

Mass of Jupiter

3

Slide 9

Doppler Effect

Source of light at rest

λ ~ 550 nm

λ ~ 550 nm

Slide 10

Doppler Effect

Source of light approaching us at high speed

λ ~ 550 nm

λ ~ 400 nm

Slide 11

Doppler Effect

Source of light receding from us at high speed

λ ~ 550 nm

λ ~ 600 nm

Slide 12

Doppler EffectThe change in the observed wavelength of radiation caused by the motion of the emitting body.

Speed of the object along the line of sight – radial velocity

Source of light moving perpendicularly to the line of sight

λ ~ 550 nm

λ ~ 550 nm

v

4

Blue light – small wavelengthRed light – large wavelength Slide 14

Doppler Effect

0

0

λλλ −

=

−=

cv

wavelengthrealwavelengthrealwavelengthshifted

lightofspeedobjectofspeed

Fig.06.05

c = λf

Large variety of wavelengths and frequencies

0

0

λλλ −

=

−=

cv

wavelengthrealwavelengthrealwavelengthshifted

lightofspeedobjectofspeed

Doppler Effect

Suppose a source of electromagnetic waves is moving away from us at 2% of the speed of light. What can be said of the wavelength of the waves we receive from the source?

A) they are blue-shifted B) they are red-shifted

5

Rotation of Mercury

Doppler Effect Speed of rotationT=C/v = 59 daysRotation W to E

1 ½ rotation about its axis for 1 orbital period

59/88 ~2/3

Edwin Hubble, 1925

Redshift in almost all galactic spectra

Universal recessional motion

The farther the object, the faster it recedes from us

Find the First Stars and Galaxies

• Need very faint objects• Fainter is the object, farther from us it is located• Object seen as it has been long time ago due to the finite speed of light

6

The most distant galaxy known

13,230 million light-years away;seen when the Universe was 470 million years young

Huge Doppler siftThe Hubble Deep Field

The retrograde motion of the planets occur naturally when the Earth passes or is passed by another planet

The retrograde motion of the planets occur naturally when the Earth passes or is passed by another planet

7

Planetary orbits and configurations

•Inner planets•Mercury•Venus

•Outer planets•Mars,•Jupiter,•Saturn,•Neptune•Uranus

Synodic Period and Sidereal Period

The time it takes for a planet to complete one orbit is called the orbital period of revolution ("orbital period" or just "period“)

We must distinguish between position with respect to Sun and position with respect to the stars when determining the period:

Sidereal period - the time it takes to return to the same position with respectto the stars, e.g. from one position on its orbit back to the same position. Sidereal period = Orbital period

Synodic period - the time it takes to return to the same position with respect to the Sun, e.g. to the same configuration.

The Giant Planets

Distance from SunRadiusVolume

318 ME95 ME14 ME17 ME

8

MassVolume

gramkglb

Averagedensity

1.3 0.7 1.3 1.6

A day is the length of time that it takes a planet to rotate on its axis (360°).

•Fast rotation10 hrs, 10 hrs,

17hrs, 16hrs

Jupiter: 0.41 days Saturn: 0.43 days Uranus: -0.69 days Neptune: 0.72 days

•Differential rotation

Tilt of the axis of rotation with respect to the ecliptic

9

All Planetary Orbits in the Solar System are Elliptical with Different Eccentricity

Pluto -- the largest EccentricityVenus – the smallest Eccentricity

Orbital Motion

↓↑

==

=

=

speedaaa

aspeedAverage

aPPa

ππ 222/3

2/3

23

Uniform circular motion