Orbital Mechanics Objectives

(Newton and Kepler)

Honors: Pgs 94-97 and 141 & 260
Advanced: pgs. 263 -266

Students will be able to:

• Define what an "Inverse Square" Law is.
• Use the generic inverse square law to solve word problems
• Define the formula for Newton's Law of Universal Gravity.
• Calculate the gravitational pull between 2 objects with mass.
• Define the relationship between "g," 9.80 m /s 2 , and The Law of Universal Gravity.
• Identify the relationship between centripetal force and gravity for orbiting satellites.
• Use the Law of Universal Gravity and Circular motion concepts to solve orbital mechanics problems.
• Define Kepler's 3 Law of Planetary motion by number .
• When given the location of one object being orbited by a satellite in an eccentric elliptical orbit, identify the location of the other orbited body.

Class Examples:

Givens: (Do not memorize.)

G = 6.673 x 10 -11 (N·m 2 )/kg 2  

Earth's Radius: 6.37 x 10 6 m            Earth's Mass: 5.98 x 10 24 kg            Orbit: 1.50 x 10 11 m

Moon's Radius: 1.74 x 10 6 m          Moon's Mass: 7.35 x 10 22 kg          Orbit: 3.85 x 10 8 m

Sun's Radius: 6.96 x 10 8 m Mass: 1.99 x 10 30 kg

1. A spaceship is traveling to a planet called Orphius. The astronauts aboard the ship have a weight of 250 N at one point in their flight. Later they are 5 times closer than when they made the first weight measurement. What will be the new weight at this closer distance?
2. On the Surface of the Earth a test pilot has a weight of 965 N. In an effort to earn her astronaut wings, our pilot travels the necessary distance of 1 000 000 ft above the Earth's surface to be recognized for astronaut wings.
1. What is the ratio of the two radii?
2. What was her weight at this altitude?
3. Calculate the value of "g" using the Earth's radius and its mass.
4. The Hubble Telescope orbits the Earth 598 km above the surface. How fast is it traveling to stay in its stable orbit?
5. At one time an infamous coputer company had an idea to put its own satellite in a low orbit   about 25 km above the Earth's Surface. How fast would these satelites travel.
6. A communications satellite stays in the same spot in the sky above the Earth's surface. It also takes 24 hours to complete a single orbit -just like the Earth's rotation. Thisorbit is unique and called a "geosynchronous orbit." How high above the Earth's surface is the satellite orbiting?