isns 3371 - phenomena of nature since gravity decreases with altitude (inversely proportional to...

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…

http://www.geo-orbit.org/sizeimgs/orbitdefr.gif


Calculating Geosynchronous Orbit Altitude

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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


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.


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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


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.


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


Tides


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.


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


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


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.


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!


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

isns 3371 - phenomena of nature since gravity decreases with altitude (inversely proportional to...

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