Goal to understand how Planetary Orbits work.

1. Goal to understand how Planetary Orbits work. Objectives: To learn about the Properties of planetary orbits To understand how orbits change 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. Planetary orbits • 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.

4. 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.

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

6. 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.

7. 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).

8. 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?

9. Velocity in an elliptical orbit • V = [GM * (2/r – 1/a)]1/2 • a is the average distance from the sun (semi-major axis). • r is the current distance from the sun

10. To get to Mars • First we need to escape from the Earth. • Since the orbital velocity is about 8 km/s this will require about 3.2 km/s. • Next we need to change our orbit (1 AU circular at 30 km/s) such that the other side goes out to the Mars’s closest point to the sun (1.38 AU) • Our average distance from the sun will be 1.19 AU as the closest and furthest points are opposite each other and our current r will be 1 AU. • So, we need to speed up to 32.3 km/s from 30 km/s • So, our total change in velocity to go from Earth orbit to Mars is only 5.5 km/s.

11. Prevent asteroid impact • If there is an asteroid which orbits from 1.02 AU to 0.98 AU then to get it to miss us forever we only need to speed it up by about 300 m/s (or roughly the cruising speed of a 747)

12. To get to (from Earth surface): • Jupiter: 20 km/s • Saturn: 21.6 km/s • Uranus: 22.6 km/s • Neptune: 22.9 km/s • Pluto: 23.1 km/s • Escape from the sun, barely, 23.2 km/s

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. Orbital time: • Time is an issue here. • Period2 = (ave dist from sun)3 • If period is in years and distance in AU • Mars: 8 months • Jupiter: 2.7 years • Saturn: 6.4 years • Uranus: 17 years • Neptune: 30 years • Pluto: 46 years (vs orbital period of ~ 250 years)

15. Conclusion • 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. • We have learned about the velocities we need to move about the solar system.