Introduction to Astronomy !AST0111-3 (Astronomía)

!!!!!!!!!!!!

Semester 2014B

Prof. Thomas H. Puzia

Newton’s Laws

Big Ball Fail!

Universal Law of Gravitation !• Every mass attracts every other mass through a force called gravity. !

• The strength of the gravitational force between two bodies is directly proportional to the mass of the two bodies.

(doubling the mass of one doubles the force). !

• The strength of gravity between two objects decreases as the square of the distance between them. Gravitational force is an inverse square law!

(doubling the distance weakens the force by 4). !!

Newton’s Laws

G = gravitational constant

= 6.67 x 10-11 m3/(kg s2)·

GravityExample: Calculate the force of the Sun above the Earth

F = GMm / r2

Where: m=6x1024kg = mass of the Earth M=2x1030kg = mass of the Sun r =1.5x1011m = Earth-Sun distance G = 6.67x10-11 m3/kg.s2 = Universal constant of Gravitation

⇒ The force of the Sun on the Earth is F = 3.6x1022 m kg/s2

!Using F=ma we can calculate the accelerations:

aEarth= F/m = 6x10-3 m/s2

aSun = F/M = 1.8x10-8 m/s2

(compare to what we feel from Earth = 9.8 m/s2)

GravityNewton: What is the force of gravity?

Force that keeps us “glued” to Earth

Force that keeps the Moon in its orbit

Force that keeps Earth bound to the Sun

Force that keeps the Sun revolving around the Milky Way

etc.

·

Gravity

·

GMp g Rp

GravityYou apparent weight on

surface of other worlds: !Earth = 80 kg

Moon = 13 kg

Mars = 30 kg

Saturn = 85 kg

Jupiter = 190 kg

Sun = 2160 kg

WD = 104.000.000 kg

NS = 11.000.000.000.000 kg

Angular Momentum !In general, L = r x p = r x mv is constant, or at least conserved in a rotating

system when no external forces are acting or when the only forces are directed toward the point of origin (central forces)

!The second law of Kepler is an example of this conservation principle.

Newton was able to derive by balancing angular momentum + gravity

P2/a3 = constant = 4π2/GM !Example: a dancer is spinning and open her arms; the rotation of a pulsar,

which was a normal star whose nucleus that collapsed. !A very important concept in Astronomy.

⇒ Formation of the solar system, planets, stars, galaxies, black holes.

Newton’s Laws

!Importance of Newton’s Laws !Understanding the movements and forces led several inventors to produce machines that profitably used those forces.

This led to the industrial revolution some 100 years after Newton's work.

We finally understood the movements in the Solar System.

!

Newton’s Laws

Key Concepts:

How did we historically come to understand the basic laws of physics and our place in our solar system?

How do we describe motion?

Functional use of Kepler’s and Newton’s laws

How is mass different from weight? What is gravity?

What is angular momentum? Why is it important?

According to the law of universal gravitation, what would happen to Earth if the Sun were somehow replaced by a black hole of the same mass

A. Earth would immediately get sucked into the black hole. B. Earth would slowly spiral into the black hole over the next few years. C. Earth’s orbit would not change. D. Earth’s orbit would become more eccentric.

Orbits

Gravitational EnergyTotal energy = Kinetic E + Potential E = constant (in closed systems)

Gravitational Binding energy is the mechanical energy required to completely separate some system. A bound system typically has a lower mechanical (kinetic) energy than its gravitational binding energy.

Kinetic Energy = 1/2 m1v2 Potential Energy = -G m1m2/R

E=∫Fdx

Example of orbitEarth and Moon

Apogee 406655k 358087km Perigee

2 Abr 11 17 Apr 11

SatellitesThe orbit of a satellite depends

on the launch velocity.

Orbits can be bound (parabolic) or unbound (hyperbolic).

Low-Earth orbit: Vcirc=8 km/s, height = 200 km, period = 90 min.

Geosynchronous Orbit: height = 36000 km, period = 1 sidereal day = 23h56m

Escape velocity: for Earth, Vesc = 11 km/s = 40000 km/h.

Note: Ve=1.4 Vcirc

for Sun, Vesc = 42 km/s = 150000 km/h. this velocity was reached by Pioneer 10/11 and Voyager 1/2.

Suppose we want to travel to Mars, and arrive with VMars.

Orbit of least energy between Earth & Mars:

a=1.26 AU (semi-major axis), P=1.4 yr, travel length 0.7 yr (0.3?).

Use VE=30 km/s, need Vsat=33 km/s.

Interplanetary travel è change of orbit = change of ship’s energy.

1.5au 1au

Mars

Earth

Launch Window: each 780 d

Interplanetary Satellites

aphelion

www.science.nasa.gov/realtime/jtrack/3d/JTrack3D.html

Positions of ~1000 satellites above the Earth in real time.

Over 6000 objects in space, only 900 of which are operational

Earth-bound Satellites

Interplanetary SatellitesAssisted orbits: e.g., Flybys of the planets by Voyager.

V = 42 km/s = 150.000 km/h

The escape velocity of an object depends on...

A. The mass of the object we are trying to escape in (e.g., a rocket) B. The mass of the body we are trying to escape from (e.g., a planet) C. How far the object is trying to travel (e.g., the Moon or another planet) D. The amount and type of energy imparted to the object E. More than one of the above.

Orbits of Binary Systems

m=M

Center of system (center of mass)

Recall: Light from moving objects will be affected by motion

m<M

Orbits of Binary Systems

m<<M

!

e.g. star with planet

Orbits of Binary Systems

Only need to see motion in star spectrum to know that planet is there

Gravitational slingshot, Gravity assist maneuver, or Swing-by

Key Concepts:

What types of orbits are there?

How can orbits be used and understood (orbital energy, Vesc, etc.)?