ISNS 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 Phenomena of Nature Calculating Geosynchronous Orbit Altitude 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 kg G= 6.67 x Nm 2 / kg 2 Plug in the numbers and you get r = 42,164 km

ISNS 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 Phenomena of Nature 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: R E = X 10 6 m, M E = 5.97 X kg, G= 6.67 x Nm 2 / kg 2 v= 11,174 m/s

ISNS 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 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 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 Phenomena of Nature Tides

ISNS 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 Phenomena of Nature The Moon pulls on tidal bulge - slows Earth’s rotation The 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 Phenomena of Nature Tidal 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 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 Phenomena of Nature Volcanic Plumes

ISNS 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 Phenomena of Nature A broad plume of gas and dust about 80 km high above a lava flow Gas and Dust Plume

ISNS Phenomena of Nature Europa Metallic core, rocky mantle, and a crust made of H 2 O 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 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 Phenomena of Nature Europa 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 Phenomena of Nature Ganymede 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