Orbital Mechanics 101, Part I

1. Orbital Mechanics 101, Part I • Understand basic orbital mechanics and how orbits work • Understand the different types of orbits used for different purposes • Understand basic principles of Interplanetary Travel mechanics

3. Newton’s Laws: Gravity • Newton’s Law of Universal Gravitation: The force of gravity between two bodies is directly proportional to the product of their two masses and inversely proportional to the square of the distance between them. • F = G M1M2 R2 • If we double the distance between the two masses (R) in the upper part of the figure to (2R) in the lower figure, the gravity force (Fg) is decreased by four (Fg/4).

4. Spheres of Influence • A body’s sphere of influence (SOI) is the surrounding volume in which its gravity dominates a spacecraft. • In theory, SOI is infinite. • In practice, as a spacecraft gets farther away, another body’s gravity dominates. • The size of a planet’s SOI depends on: • The planet’s mass • How close the planet is to the Sun (Sun’s gravity overpowers that of closer planets)

5. Escape Velocity • Because a body’s size and mass determine its gravitational pull, escape velocity differs for each object as explained by our pal Newton F = G M1M2 R2 ….Or just think of a baseball

6. Orbital Motion: Baseballs in Orbit 8 Km • If a baseball player throws a baseball horizontally from a mountain top: • Gravity pulls the ball toward the ground. • The faster a ball is thrown horizontally, the farther it will go before gravity pulls it to the ground. • When an object moves fast enough, it will go far enough as it falls to “miss” the Earth and stay in orbit. 5 m

7. Orbital Motion: Baseballs in Orbit 12 Km/sec 12 Km/sec D 8 Km/sec 8 Km/sec G 5 Km/sec 5m 5 Km/sec 5m 5m For that second of travel, gravity will pull the baseball approximately 5 meters towards the earth For every 8Km traveled the earth’s surface given that it is curved, drops 5 meters from under the object in motion So if my baseball is traveling 8Km/sec the distance downward caused by gravity is offset by the curvature drop-off of the earth, hence…. An orbit is sustained

8. Orbital Motion: Baseballs in Orbit • Therefore, a baseball thrown fast enough to cover exactly 8 kilometers in the time it takes the ball to fall 5 meters will be in a circular orbit. • Increasing velocity (adding more energy) will make it an elliptical orbit, unless escape velocity is reached

9. Orbital Velocity • Orbital velocity – the speed an object must maintain to stay in orbit • The closer an object is to Earth, the faster it needs to travel to remain in orbit • The higher a spacecraft climbs from Earth, the slower it can travel and still resist gravity At an altitude of 124 miles the required orbital velocity is just over 17,000 mph (about 27,400 kph). To maintain an orbit that is 22,223 miles above Earth, the satellite must orbit at a speed of about 7,000 mph . That orbital speed and distance permits the satellite to make one revolution in 24 hours.

10. Orbiting Around a Soda Can • On top we have an orbit around a soda can. • If we draw a line on the soda can directly below the orbit we’d get a ground track. • If we cut the soda can in half and laid it flat, the shape of the ground track is as shown in the lower figure.

11. Non-Rotating Earth • Here’s what a ground track would look like for a non-rotating Earth if we stretch the Earth onto a flat-map projection. • Notice that the ground track is made by a spacecraft in orbit around Earth—this orbit is a great circle.

12. Add Earth’s Rotation Non-Rotating Earth • This is a typical low Earth orbit. • The “map” moves eastward so the second orbit ground track looks like it moved to the west. Rotating Earth

13. Types of Orbits • Low-Earth orbit – an orbit up to about 1,240 miles above the Earth • Medium-Earth orbit– one with an altitude of about 12,400 miles • High-Earth orbit – an orbit at an altitude of about 22,300 miles

14. Types of Orbits • Low Earth Orbit (LEO) • Lowest altitude a spacecraft must achieve to in order to orbit the Earth (520 km altitude ) • Spacecraft in these orbits circle the Earth approximately every 90 minutes or so. • Used for things that we want to visit often like the Hubble Space Telescope and the International Space Station • A significant disadvantage is the speed of the satellite which at 18,000 miles per hour in LEO does not spend very long over any one part of the Earth at a given time. Apogee Perigee

15. Types of Orbits • Polar Orbits • These orbits have an inclination near 90 degrees. • This allows the satellite to see virtually every part of the Earth as the Earth rotates underneath it. • It takes approximately 90 minutes for the satellite to complete one orbit. 90 deg

16. Types of Orbits • Geosynchronous (Geostationary) Orbits (GEO) • Orbits with a period of about 24 hours. • Since it matches the revolution cycle of the earth, it holds stationary over a given point of the earth’s surface • Disadvantage is the expense in putting a satellite into high orbit nor is it possible to repair it via the space shuttle. • Geosynchronous orbit is over Earth’s equator and is called a Geostationary orbit

17. Types of Orbits

18. Orbital Mechanics 101, Part I • Understand basic orbital mechanics and how orbits work • Understand the different types of orbits used for different purposes