1. Goal to understand how the solar system works.
Objectives:
To learn about the Properties of planets
To understand how orbits work
To understand how Orbital velocities are determined
To understand what Escape velocity is and how it compares to the orbital velocity

2. 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?

3. 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.

4. 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.

5. Magnetic Field
Some planets have a magnetic field. The strength of the field tends to depend on the rotation rate of the planet.

6. 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.

7. 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.

8. Derive Kepler’s 3rd law:
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

9. Changing Orbits
What happens though when you change the velocity (from a collision, or a spaceship blasting off from the surface)?

10. 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.

11. 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).

12. 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).

13. 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.

14. 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?

15. 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.