Post on 15-Jan-2016
transcript
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
Newton’s Law of GravityNewton’s Law of GravityKepler’s 3rd LawKepler’s 3rd Law
€
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
Newton’s Law of GravityNewton’s Law of GravityKepler’s 3rd LawKepler’s 3rd Law
€
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
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P 2 =1
MS
A3
In general, In general, in units of AU, years, solar massesin units of AU, years, solar masses
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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
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(6x10−4 )2 =1
Mearth
(10−4 )3
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3.3x105 =1
Mearth
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Mearth = 3x10−6Mo =1/300,000 Solar Masses
AstronauticsAstronautics
AstronauticsAstronautics
AstronauticsAstronautics
• What makes rockets go?What makes rockets go?• Newton’s 3rd LawNewton’s 3rd Law
AstronauticsAstronautics
AstronauticsAstronautics
• 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.
AstronauticsAstronautics
• Before launch, the vast majority of mass to lifted is fuel!Before launch, the vast majority of mass to lifted is fuel!
AstronauticsAstronautics
QuickTime™ and aYUV420 codec decompressorare needed to see this picture.
AstronauticsAstronautics
Launch TrajectoryLaunch Trajectory
Earth
AtmosphereAtmosphere(not to scale)(not to scale)
AstronauticsAstronautics
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
ConcepTest!ConcepTest!
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
ConcepTest!ConcepTest!
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
ConcepTest!ConcepTest!