Transcript powerpoint - Physics @ IUPUI

Goal to understand how the
solar system works.
Objectives:
1) To learn about the Properties of planets
2) To understand how orbits work
3) To understand how Orbital velocities are
determined
4) To understand what Escape velocity is
and how it compares to the orbital
velocity
Question:
• It takes 8 km/s to go from the surface of
the earth to Earth orbit. How much
velocity do you think you need to go from
Earth orbit to get to Mars?
Properties of planets
• All planets have components.
• All planets have a core. The size of the core differs
from planet to planet, but most are made of iron.
• Most have a mantle.
However, the size and
makeup of the mantel
varies.
• Not all have a crust like
we know it.
• Some have an
atmosphere, but the size
and composition vary.
Atmosphere
• Atmosphere’s vary. Some planets are mostly
atmosphere.
• A common theme is “pressure”.
• Pressure is just the weight of the stuff above you
(on earth that weight is the weight of 10 meters
of water).
• So, if you dive down 10 meters under the water,
the pressure will be 2 bars (1 from the air, and 1
from the water).
• Most sizable atmospheres have clouds and
storms.
Magnetic Field
• Some planets have a magnetic field. The
strength of the field tends to depend on
the rotation rate of the planet.
Planetary orbits
• As we saw from Kepler’s first law, orbits
are elliptical.
• Orbits are usually very stable.
• While the orbit will change a little with time
due to outside influences (such as
Jupiter), mostly they stay the same.
• So, an object in the asteroid belt tends to
stay there, and won’t hit us.
Near circular orbits:
• For a given object (such as the earth, moon, or sun)
there will be a velocity at which you will have a circular
orbit (although this velocity depends on your distance
from the object).
• Vorbit = (G M / r)1/2
• Where G is a constant, M is the mass of the object you
are orbiting, and r is the distance away from that object.
• So, the orbital velocity is faster when you get closer to
the object, and slower as you get further away.
• The earth’s orbital velocity around the sun is 30 km/s.
• The orbital velocity around the earth at an altitude of
about 120 miles is about 10 km/s. The orbital velocity at
the orbit of the moon is about 1 km/s.
Derive Kepler’s 3rd law:
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•
•
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V = (GM / R)1/2
P = 2π R / V
P2 = (2π R)2 / V2
P2 = (4π2 R2) * R / GM
P2 = (4π2/GM) a3
k = 4π2/GM
So, P2 = k a3
Changing Orbits
• What happens though when you change
the velocity (from a collision, or a
spaceship blasting off from the surface)?
Orbital change
• The object will always come back to it where it
started (assuming that it does not escape).
• The change will be that another part of the orbit
will move (outward if you speed up the object,
and inward if you slow it down).
• The location of the change depends on the
direction of the velocity change.
• If it is in the direction of orbit, it will be the far
side of the orbit.
To go somewhere:
• If you are setting up a space mission, you
set up your orbit so that it starts at earth
(and would come back to that spot –
hopefully when the earth is there), and
have it reach its furthest out when it gets
to the object you want to go to (such as
Mars).
To get to Mars:
• To get to Mars, it take about half the difference in
velocity of the Earth’s orbit and Mars’s orbit.
Add to that the amount you need to escape from
the earth.
• The best time to get to Mars is when it is at its
closest point to the sun.
• To do this, you need about 8 km/s (3.2 km/s to
escape from Earth, and 5 km/s to go from the
earth’s orbit to an orbit which intersects Mars).
Orbit terms:
• Perihelion – the point of the orbit closest to the sun
• Perigee - the point of the orbit closest to the earth
• Aphelion - the point of the orbit furthest from the
sun
• Apogee - the point of the orbit furthest from the
earth
• Major axis – the longest length of the orbit
• Minor axis – the shortest length of the orbit
• Eccentricity – a measure of how elliptical the orbit
is.
Escape velocity
• If you go from the circular orbit and increase the
velocity (as we did in the homework), your craft
will move further and further out in the other side
of the orbit (and come back to where it started).
• At some point, however, the craft would go
infinitely far. This is the escape velocity.
• Vescape = Vorbit * 21/2
• Name some objects in our solar system which
are currently traveling at faster then the escape
velocity of the sun?
Conclusion
• We have seen the components of the
planets we will be looking at later.
• We examined orbits and saw that
changing the orbit will change the other
half of the orbit.
• We saw that you can escape if fast
enough, or you can fine tune it to go from
1 object to another.