Download Everything from Velocity, Seasons, Tides

Everything in Orbit
Orbital Velocity
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Orbital velocity is the speed at which a planetary body moves in its orbit around another body. If orbits were circular, this velocity would be constant. However, from discussion of Kepler’s Laws, we know that planetary bodies orbit the sun (or their planet) in elliptical paths. Therefore, when the planetary body is closer to the sun in their orbit (perihelion), it actually moves faster than it does when it is farther away due to gravitational force
 Equation of orbital velocity: v2=GM(2/r­1/a) where: G is the gravitational constant (G=6.67x10­11 N/m3 kg), M is the mass of the sun (or central body), r is the body’s distance from the sun,
a is the semi major axis
 If the orbit is circular, r=a, and the equation reduces to v2=GM/R
 The orbits of most of the planets, especially the inner planets are nearly circular, and can be treated as such
Another thing about Orbital Velocity…
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Why don’t objects spiral into the sun?
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The body has a particular orbital velocity, thus it has a certain inertia (a force that tries to keep the body going in a straight line). The body’s inertia exactly equals the gravitational force.
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If for some reason the body slowed down or lost energy, it would crash into the Sun
Application: satellites
We can put satellites in any orbit around the Earth, but inertia must equal gravitational force to keep it in orbit
 That means closer satellites must orbit the Earth faster because there is a larger gravitational force to overcome
 For example: weather satellites orbit at a distance of 35,786 km and have an orbital velocity (assuming circular orbit) of 11,300kmph
But other satellites (i.e., Landsat) orbit the Earth at a distance of 800km with an orbital velocity of 80,317kmph
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Escape Velocity
If we launched a satellite with so much speed, inertia would overcome gravity and the satellite would achieve escape velocity
 Escape velocity = “speed required to project a body completely free of a primary body” (Hartmann 1999)
 Equation:
V=(2GM/R)1/2 where: G=gravitational constant
M=Earth or primary body mass
R=Earth or primary body radius
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Planetary Escape Velocity
Primary Body
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Escape Velocity
4.4 km/sec
10.4 km/sec
11.2 km/sec
5.0 km/sec
59.5 km/sec
35.5 km/sec
21.3 km/sec
23.5 km/sec
1.1 km/sec
Applications of Escape Velocity
 Meteorites  Atmospheres
 Voyager: to the edge of the Solar System
Orbital Energy
 Total orbital energy of an orbiting body is conserved. This means:
­orbiting body will not spontaneously fly off into space!
­orbiting body will follow same path around central body, with same orbital velocity unless perturbed in some way
Tidal Forces­The Earth­Moon System
 Tidal forces between the Earth and Moon are an application of orbital energy­ the Moon will NOT follow the same orbital path forever because it is perturbed by gravitational forces between the two planetary bodies
Earth Tides
 Gravitational attraction greater on side that faces the moon
 Earth “stretches” along Earth­Moon line
 Oceans fluid and can move in response to this stretching, creates tidal bulges, or high and low tides
 Two special tides: spring tides and neap tides.  Spring tides: tidal force of Moon and Sun on Earth add to get stronger tides
 Neap tides: tidal force of Moon and Sun cancel to get weaker tides
Consequences of Tides
 Force of oceans flexing creates a lot of friction
 Over the history of the Earth, this friction has actually slowed the Earth’s rotation down
 Conservation of angular momentum: Earth loosing momentum, Moon gains it!
 Result: Moon is spinning out into a larger orbit!
Moon Tides
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Interaction with Earth also created bulge on Moon, but Moon solidified, so bulge is frozen in Moon
Long axis of Moon always pointed toward Earth
In order to keep this orientation, Moon rotates once during the time it orbits the Earth once: “synchronous rotation”
Consequence: Moon always has the same side toward Earth
Tidal Forces­ The Jupiter­Io System
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Tidal effects on Io creates a tidal bulge
gravitational perturbation from other Galilean satellites causes Io’s orbit to be more elliptical
Io pulled differently depending on distance from Jupiter
This “flexing” is enough to heat Io’s interior, called “tidal heating”
Result: Io is most volcanically active planetary body!
Tidal Forces­Saturn’s Rings
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Gravitational forces increase the closer you are to a body
There’s a critical limit within which tidal forces overcome the satellites’ own gravity, tearing it apart
This limit is known as Roche’s Limit
Phases of the Moon Eclipses
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Two types: Solar and lunar eclipses
Solar eclipse: Moon’s path moves in front of Sun, blocking it out
Lunar eclipse: Earth moves between Sun and Moon, appears red from sunlight filtering through Earth’s atmosphere
Eclipses
Morning Star, Evening Star
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Because Venus is closer to the Sun, it can never appear to be far away from the Sun in the sky. We can’t see it in the day because Sunlight blocks it out, but we can see it as the Sun either sets or rises
Mercury behaves the same way, but Venus is much brighter
Lagrangian Points
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Three body problem, interaction between Moon’s and Earth’s gravity
In such a system, there are 5 points where the gravitational forces balance each other
A body at one of those points would be stable and stationary
Trojan asteroids: in L4 and L5 spots for Sun­Jupiter system
Seasons
 Seasons due to tilt of Earth’s axis and elliptical orbit
 For example, winter in Northern Hemisphere: closer to sun, but axis pointed
away from
sun