Bit of Administration …. 6-Week Test6-Week Test –TONIGHT! 7:15-8:30, 3425 Sterling –55...

Bit of Administration ….Bit of Administration ….

• 6-Week Test6-Week Test– TONIGHT! 7:15-8:30, 3425 SterlingTONIGHT! 7:15-8:30, 3425 Sterling– 5555 multiple choice questions multiple choice questions

• 2/3 conceptual use of the material2/3 conceptual use of the material• 1/3 recall1/3 recall

– All material in lecture, discussion, homeworksAll material in lecture, discussion, homeworks through Wednesday; readings on that materialthrough Wednesday; readings on that material

• ReadingReading– Download NASA article from www.astro.wisc.edu/astro104Download NASA article from www.astro.wisc.edu/astro104

Newton’s Law of GravityNewton’s Law of Gravity

11 22FgFg

M1 = Mass of object 1 (grams)

M2 = Mass of object 2 (grams)

D = Distance between objects (cm)

G = 6.67x10-8 cm3/sec2/gm

D

€

Fg =GM1M2

D2

Newton’s Law of GravityNewton’s Law of GravityKepler’s 3rd LawKepler’s 3rd Law

A

SP

In order for planet P to travel in a circle around the Sun…In order for planet P to travel in a circle around the Sun…

Central Force = Gravitational ForceCentral Force = Gravitational Force

€

M pVp2

A=GMSM p

A2

€

Vp2

A=GMS

A2

€

Vp2 =GMS

A

Velocity depends only on distance,Velocity depends only on distance,not on mass of planetnot on mass of planet

Velocity decreases w. greater distanceVelocity decreases w. greater distance


€

Vp2 =GMS

A

€

Vp =distance

time=

2πA

P

€

4π 2A2

P 2=GMS

A

€

4π 2A3

P 2=GMS

€

4π 2A3 =GMSP2

€

4π 2

G

A3

MS

= P 2

€

P 2 =4π 2

G

1

MS

A3

A

CP


€

P 2 =4π 2

G

1

MS

A3 In general, In general, in units of cm, sec, gmsin units of cm, sec, gms

€

(1yr)2 =4π 2

G

1

Mo

(1AU)3

For the EarthFor the Earth

€

P 2 =1

MS

A3

In general, In general, in units of AU, years, solar massesin units of AU, years, solar masses

€

P 2 = A3 For objects orbiting the Sun (MFor objects orbiting the Sun (Mcc = 1 M = 1 Moo))

A

CP

1 Solar Mass1 Solar Mass

Nature and nature’s lawsNature and nature’s lawsLay hid in the nightLay hid in the night

God said, “Let Newton be!”God said, “Let Newton be!”And all was light!And all was light!

- - Alexander PopeAlexander Pope

Newton’s Law of GravityNewton’s Law of GravityKepler’s 3rd Law - General Form for MKepler’s 3rd Law - General Form for Mcentralcentral >> M >> Morbiting objectorbiting object

P = Period of Orbit (years)

A = Semi-Major Axis of Orbit (AU)

Mc = Mass of central body (Solar Masses, Mo)

€

P 2 =1

Mc

A3

A

C

orb

Newton’s Law of GravityNewton’s Law of GravityKepler’s 3rd Law - Weighing the Solar SystemKepler’s 3rd Law - Weighing the Solar System

€

P 2 =1

Mc

A3

A

Suppose a satellite is in orbit 8600 km above the Earth’s surface.Suppose a satellite is in orbit 8600 km above the Earth’s surface.Its period is 0.2 days. What is the mass of the Earth?Its period is 0.2 days. What is the mass of the Earth?

A = 15,000 km = 10-4 AU (Earth radius is 6400 km)P = 0.2 days = 6 x 10-4 yr

€

(6x10−4 )2 =1

Mearth

(10−4 )3

€

3.3x105 =1

Mearth

€

Mearth = 3x10−6Mo =1/300,000 Solar Masses

AstronauticsAstronautics


• What makes rockets go?What makes rockets go?• Newton’s 3rd LawNewton’s 3rd Law


• Burn fuel to create hot gasBurn fuel to create hot gas• Allow gas to escapeAllow gas to escape• Action of escaping gas => reaction of rocket motionAction of escaping gas => reaction of rocket motion

• Important! The rocket does not push against anything -Important! The rocket does not push against anything - this physics equally valid in the vacuum of spacethis physics equally valid in the vacuum of space

• What makes rockets go?What makes rockets go?• Newton’s 3rd LawNewton’s 3rd Law

QuickTime™ and aCinepak decompressorare needed to see this picture.


• Before launch, the vast majority of mass to lifted is fuel!Before launch, the vast majority of mass to lifted is fuel!

QuickTime™ and aYUV420 codec decompressorare needed to see this picture.


Launch TrajectoryLaunch Trajectory

Earth

AtmosphereAtmosphere(not to scale)(not to scale)


Launch TrajectoryLaunch Trajectory

Earth

Earth Rotation

Earth Rotation10,800 km/hr

10,800 km/hr

AstronauticsAstronauticsLaunch TrajectoryLaunch Trajectory

into Orbitinto Orbit

Earth

Earth Rotation

Earth Rotation10,800 km/hr

10,800 km/hr

28,800 km/hr28,800 km/hrfor orbitfor orbit

at Earth’s surfaceat Earth’s surface

QuickTime™ and aYUV420 codec decompressorare needed to see this picture.

In you were going to point in the direction that the Earth is In you were going to point in the direction that the Earth is rotating*, you would point rotating*, you would point

A) To the EastA) To the East B) To the WestB) To the West

* Or put another way, the direction that you are moving right * Or put another way, the direction that you are moving right now because of the rotation of the Earth.now because of the rotation of the Earth.

ConcepTest!ConcepTest!

Cape CanaveralCape CanaveralEarth RotationEarth Rotation

10,800 km/hr10,800 km/hr

AstronauticsAstronautics• Special OrbitsSpecial Orbits

GeosynchronousGeosynchronous36,000 km36,000 km

Mid-Earth OrbitMid-Earth Orbit20,000 km20,000 km

Low-Earth OrbitLow-Earth Orbit200 km200 km

NP

In which orbit does a satellite have the longest period? In which orbit does a satellite have the longest period?

A) Low-Earth orbitA) Low-Earth orbit B) Mid-Earth orbitB) Mid-Earth orbit C) Geo-synchronous orbitC) Geo-synchronous orbit D) Depends on the mass of the satelliteD) Depends on the mass of the satellite


AstronauticsAstronautics• Special OrbitsSpecial Orbits GeosynchronousGeosynchronous

36,000 km36,000 km24 hrs24 hrs

Weather, SurveillanceWeather, Surveillance

Mid-Earth OrbitMid-Earth Orbit20,000 km20,000 km

12 hrs12 hrsGPS, CommunicationsGPS, Communications

Low-Earth OrbitLow-Earth Orbit200 km200 km90 min90 min

Space Shuttle, Hubble Space TelescopeSpace Shuttle, Hubble Space Telescope

NP

In which orbit is a satellite moving faster? In which orbit is a satellite moving faster?

A) Low-Earth orbit (Space Shuttle)A) Low-Earth orbit (Space Shuttle) B) Mid-Earth orbit (GPS satellites)B) Mid-Earth orbit (GPS satellites) C) Geo-synchronous orbit (Weather satellites)C) Geo-synchronous orbit (Weather satellites) D) Depends on the mass of the satelliteD) Depends on the mass of the satellite


AstronauticsAstronautics• Special OrbitsSpecial Orbits

Mid-Earth Polar OrbitMid-Earth Polar Orbit20,000 km20,000 km

12 hrs12 hrsSpy Satellites, GPSSpy Satellites, GPS

Cape CanaveralCape CanaveralEarth RotationEarth Rotation

10,800 km/hr10,800 km/hrVandenberg AFBVandenberg AFB

If you are going to launch a satellite into a polar orbit from If you are going to launch a satellite into a polar orbit from Vandenberg AFB, in which of these directions would you Vandenberg AFB, in which of these directions would you launch? launch?

A) SoutheastA) Southeast B) SouthB) South C) SouthwestC) Southwest D) WestD) West


Bit of Administration …. 6-Week Test6-Week Test –TONIGHT! 7:15-8:30, 3425 Sterling –55...

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