Laws describing the planetary motion. Weight and acceleration due to gravity. Calculating the mass of Earth (6378 M G

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1 Laws describing the planetary motion Kepler s Laws a Newton s Laws Speed, velocity, acceleration, force, inertia, mass, balanced and unbalanced forces Weight and acceleration due to gravity 1. Weight gravitational force attracting an object to the.. How much is the weigh depends on how strong is the gravitational field of the planet W F F grav grav m a m G F ma Law of Universal Gravitation m F G d G a 9.81 m / s W m g a g Acceleration due to gravity easured for objects in free fall Calculating the mass of Newton s version of Kepler s rd empirical law: G 678 km G g 9.81m / s 11 N m /kg 4π a G( m + ) a m G g ( ) kg Fundamental Astronomical constant Units: - in seconds, a - in meters. Allows to calculate masses

2 Gravitational Force 4π a G( m + ) in seconds a in meters Week force: F G m d G6.67x10-11 Nm /kg m 1kg d 1m 79a ( m + ) in days instead of seconds a in meters F G6.67x10-11 N 79a of Jupiter is much larger than m of Satellite. 79a in days a in meters ass of Jupiter Io 79a 1.77 days a km kg

3 Source of light at rest Source of light approaching us at high speed λ ~ 400 nm Slide 9 Slide 10 The 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 receding from us at high speed Slide 11 λ ~ 600 nm Slide 1 v Source of light moving perpendicularly to the line of sight

Blue light small wavelength ed light large wavelength Slide 14 speed of object shifted wavelength real wavelength speed of light real wavelength v λ λ0 c λ 0 c λf Large variety of wavelengths and

4 Blue light small wavelength ed light large wavelength Slide 14 speed of object shifted wavelength real wavelength speed of light real wavelength v λ λ0 c λ 0 c λf Large variety of wavelengths and frequencies 0 Fig speed of object shifted wavelength real wavelength speed of light real wavelength v λ λ0 c λ Suppose a source of electromagnetic waves is moving away from us at % 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

otation of ercury Speed of rotation TC/v 59 days

orbital period 59/88 ~/ Edwin Hubble, 195 edshift in

motion The farther the object, the faster it recedes

faint objects Fainter is the object, farther from us it

5 otation of ercury Speed of rotation TC/v 59 days otation W to E 1 ½ rotation about its axis for 1 orbital period 59/88 ~/ Edwin Hubble, 195 edshift 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

1,0 million lightyears away; seen when the Universe was

Doppler sift The Hubble Deep Field The retrograde motion

passed by another planet The retrograde motion passed by

6 1,0 million lightyears away; seen when the Universe was 470 million years young The most distant galaxy known Huge Doppler sift The Hubble Deep Field The retrograde motion of the planets occur naturally when the passes or is passed by another planet The retrograde motion of the planets occur naturally when the passes or is passed by another planet

lanetary orbits and configurations Inner planets ercury Venus Outer planets ars, Jupiter, Saturn, Neptune Uranus Synodic eriod and Sidereal eriod The time it takes for a planet to complete one

determining the period: Sidereal period - the time it takes to return to the same position with respect to the stars, e.g. from one position on its orbit back to the same position.

7 lanetary orbits and configurations Inner planets ercury Venus Outer planets ars, Jupiter, Saturn, Neptune Uranus Synodic eriod and Sidereal eriod 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 respect to 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 lanets 18 E 95 E 14 E 17 E Distance from Sun adius Volume

respect to the ecliptic Fast rotation 10

8 ass Volume gram kg lb Average density A day is the length of time that it takes a planet to rotate on its axis (60 ). Tilt of the axis of rotation with respect to the ecliptic Fast rotation 10 hrs, 10 hrs, 17hrs, 16hrs Jupiter: 0.41 days Saturn: 0.4 days Uranus: days Neptune: 0.7 days Differential rotation

Eccentricity Venus the smallest Eccentricity Orbital

9 All lanetary Orbits in the Solar System are Elliptical with Different Eccentricity luto -- the largest Eccentricity Venus the smallest Eccentricity Orbital otion Uniform circular motion a a / Average speed a speed π a π / a a

Observational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws

Observational Astronomy - Lecture 4 Orbits, Motions, Kepler s and Newton s Laws Craig Lage New York University - Department of Physics craig.lage@nyu.edu February 24, 2014 1 / 21 Tycho Brahe s Equatorial