isns 3371 - phenomena of nature since gravity decreases with altitude (inversely proportional to...
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ISNS 3371 - Phenomena of Nature
Since gravity decreases with altitude (inversely proportional to square of distance from the center of the Earth), the orbital velocity varies with altitude.
Geosynchronous/Geostationary Orbits
A geostationary orbit is 42,000 km above the center of the Earth and the altitude is about 35,600 km
A geosynchronous orbit has a period the same as the rotational speed of the Earth - e.g., it orbits in the same amount of time that the Earth rotates - 1 sidereal day. A geostationary orbit is a geosynchronous orbit at the equator - it always stays above the same place on the Earth - communications satellites, satellite TV, etc…
ISNS 3371 - Phenomena of Nature
Calculating Geosynchronous Orbit Altitude
€
Fcentripetal = Fcentrifugalmsatag = msatacag = ac
ac =ω2r
ag =MG
r2
ω2r =MG
r2
r3 =MG
ω2
r =MG
ω23
For an orbiting body, the inward and outward forces must equal each other (Newtons 3rd Law) - the centripetal force from orbital motion has to equal the centrifugal force from gravity:
is angular velocity - at geosynchronous orbit, of satellite is equal to the angular velocity of the Earth
= 2/86164 (length of sidereal day)M = 5.97 X 1024 kgG= 6.67 x 10-11 Nm2/ kg2
Plug in the numbers and you get
r = 42,164 km
ISNS 3371 - Phenomena of Nature
Escape Velocity
If a projectile is fired straight up with a large enough velocity, it will escape the Earth’s gravity. It will travel slower and slower due to the Earth’s gravity, but never to zero. Escape velocity - velocity at which gravity can not stop outward motion. Note that the gravitational attraction of Earth never ceases, it just gets infinitesimally small.
Escape velocity is calculated by using conservation of energy - a body achieves escape velocity when the all of its initial gravitational energy is converted to kinetic energy.
ISNS 3371 - Phenomena of Nature
€
PE(at Earth's surface) = mgh = mgRE
g =GME
RE
PE =GMEm
RE
KE =1
2mv 2
1
2mv 2 =
GMEm
RE
v =2GME
RE
Gravitational potential energy at the Earth’s surface
Acceleration due to gravity
Potential energy
Kinetic energy
KE=PE
Escape velocity
Starting from the surface of the Earth:
RE = 6.378 X 106 m, ME = 5.97 X 1024 kg, G= 6.67 x 10-11 Nm2/ kg2
v= 11,174 m/s
ISNS 3371 - Phenomena of Nature
Center of Mass
Newton also showed that two objects attracted to each other by gravity actually orbit about their center of mass - the point at which the objects would balance if the were connected.
This idea is used to find planets orbiting other stars - massive planets cause star to move against background stars
Center of Mass - Binary Star
ISNS 3371 - Phenomena of Nature Tides
The gravitational attraction of the Moon varies as the square of the distance (Newton’s Law of Gravitation) - gravity stronger on side facing the Moon than on opposite side. The Moon pulls the ocean water towards it on facing side - creates tide - and pulls the Earth away from the ocean water on the other side - reason for tides twice a day. Time of tides varies by 50 min per day - Moon at its highest point every 24 hrs 50 min because Moon orbits Earth while Earth rotates.
ISNS 3371 - Phenomena of Nature
The Sun also causes tides - why are they weaker than the Moons’ (by about 1/2)? The Sun’s gravitational attraction on the Earth is about 180 times that of the moon. But the Sun’s greater distance means the difference on opposite sides of the Earth is much smaller - only about 0.02% as opposed to 7% for the moon.
Neap tides - when Moon’s and Sun’s gravitational forces oppose each other
Spring tides - when Moon’s and Sun’s gravitational forces add up
ISNS 3371 - Phenomena of Nature
Tides
ISNS 3371 - Phenomena of Nature
Tidal Bulge
Because the Earth rotates, friction drags the tidal bulges off of the Earth-Moon line. This tidal friction causes the Earth’s rotation to slow and the Moon to move farther out.
ISNS 3371 - Phenomena of Nature
The Moon pulls on tidal bulge - slows Earth’s rotationThe excess mass in Earth’s tidal bulge exerts a gravitational attraction on the Moon that pulls the Moon ahead in its orbit - Moon moves farther away -
Conservation of Angular Momentum!
ISNS 3371 - Phenomena of NatureTidal Heating in Jovian Moons
The four inner moons of Jupiter - Io, Europa, and Ganymede - all show evidence of geological activity - indicators of molten interiors. The heat source is tidal heating.Moons have elliptical orbit and synchonous rotation - one side always faces Jupiter
- as Ganymede completes one orbit, Europa completes exactly two orbits, and Io completes exactly four orbits - moons periodically line up - causes orbital ellipticity.
- tidal bulges are constantly being flexed in different directions - generates friction inside
ISNS 3371 - Phenomena of Nature
Io
Jupiter’s tidal forces flex Io like a ball of silly putty.
- friction generates heat
- interior of Io is molten
Volcanoes erupt frequently.
- sulfur in the lava accounts for yellow color
- surface ice vaporizes and jets away
Evidence of tectonics and impact cratering is covered.
ISNS 3371 - Phenomena of NatureVolcanic Plumes
ISNS 3371 - Phenomena of Nature
Lava fountain - active lava hot enough to cause "bleeding" in Galileo's camera - overloading of camera by the brightness of the target
Newly erupted hot lava flow. Dark, "L"-shaped lava flow marks the location of the November 1999 eruption.
ISNS 3371 - Phenomena of Nature
A broad plume of gas and dust about 80 km high above a lava flow
Gas and Dust Plume
ISNS 3371 - Phenomena of NatureEuropa
Metallic core, rocky mantle, and a crust made of H2O ice
Its fractured surface tells a tale of tectonics.
- few impact craters seen
- double-ridged cracks
- jumbled icebergs
These provide photographic evidence of a subsurface ocean.
Europa has a magnetic field.
- implies liquid salt water beneath the icy crust
Where liquid water exists, there could be life!
ISNS 3371 - Phenomena of Nature
ISNS 3371 - Phenomena of Nature
Evidence of a Subsurface ocean
Jumbled crust with icebergs and surface cracks with double-ridged pattern - caused by tidal flexing of thick layer of ice on top of liquid ocean of water.
ISNS 3371 - Phenomena of NatureEuropa Ice Rafts
Thin, disrupted, ice crust in the Conamara region of Europa - white and blue colors outline areas blanketed by a fine dust of ice particles ejected at the time of formation of the large (26 kilometer in diameter) crater Pwyll 1000 kilometers to the south. - a few small craters - less than 500 meters in diameter were probably formed at the same time as the blanketing occurred by large, intact, blocks of ice thrown up in the impact explosion that formed Pwyll.
ISNS 3371 - Phenomena of NatureGanymede
Largest moon in the Solar System
Its surface has 2 types of terrain:
- heavily cratered, implies old
- long grooves, few craters, implies young like Europa
It also has a magnetic field.
Could it have subsurface ocean?
- case not as strong as Europa’s
- tidal heating would be weaker
- would need additional heating from radioactive decay