Satellite Physics & Planetary Motion Illustration from Isaac Newton, Philosophiae Naturalis Principia Mathematica, Book III Isaac Newton was the first to argue that if a projectile is given enough velocity, it would fall _______ the earth rather than into it!! The projectile is then called a ________ and the trajectory is called an ______. around satellite orbit

Newton’s Cannon So as previously mention Newton that if a projectile is given enough velocity, it would fall around the earth rather than into it!! Check out this animation of Newton’s Cannon

So, what is the ONLY force acting on a satellite (moons or man-made)? The _____________ force between the satellite and planet it’s orbiting (which would equal the ______ of the satellite at that point). If the orbit is a circular orbit, then, the gravitational force is the ___________ force. (Note that the direction of the gravitational force on the satellite is always towards the center of the planet - it’s “center-seeking”!) gravitational weight centripetal

But, wait…. If the force of gravity (or weight ) is the only force acting on a satellite, why do astronauts experience what is known as “weightlessness” (they appear to be floating!) when in orbit? Actually they are ______________!! Gravity is NOT zero there (or they wouldn’t stay in orbit!). They and the space shuttle are BOTH ______. It would be more accurate to say: They are experiencing “____________________” or “apparent weightlessness”! NOT weightless falling normalforcelessness

So, if gravity is the ONLY force acting on the satellite, why doesn’t the satellite “fall” and hit the earth? Remember that it ________.... In order for a satellite to be moving in a circular orbit, it must be traveling at just the right ______ to ___________ ___________ IS falling! velocityfall around the earth

We can calculate the required velocity, v, for a satellite’s circular orbit: Earth V (NOT a force) F c =W R R = radius of orbit (distance from center of earth) Mass of satellite cancels out and is thus ___________! What happens if ? ________ orbit! irrelevant elliptical

The speed of a satellite orbiting near the earth’s surface can then be easily calculated since we know g and R… In order to calculate the speed of a satellite orbiting at a larger radius, we must first find the acceleration of gravity, g, at that radius…. Isaac Newton again provides us the with the key. He showed that the gravitational force between two masses ________ as the distance between them increases. In other words, it’s an _______ relationship… g ___ as R ↑. decreases inverse ↓

“Newton’s Law of Gravitation” He formulated the relationship as a mathematical equation for the gravitational force: Where… m 1 and m 2 are the masses R = distance between masses G = the Gravitational Constant It’s evident from the equation that the force is not just inversely proportional to the distance, but inversely proportional to the SQUARE of the distance. So, g, the acceleration of gravity, also follows what is known as an “______________ law” means “proportional to” inverse square

An example using Earth R = 2R E R = 3R E If R = 2R E (R is doubled) g = _________________ If R = 3R E (R is tripled) g = _________________ If R = 60R E (approximate distance to the moon) g = ___________ Note: This is NOT the value of “moon’s gravity”!) Very small, but enough to cause our tides!!

R 3.8 x10 8 m 7.36 x10 22 kg 5.97 x10 24 kg (6.67E-11)(7.36 x10 22 kg) (5.97 x10 24 kg) ((3.8 x10 8 m) 2) 2.03 x10 20 N G is the gravitational constant = 6.67E-11

Kepler’s Laws

Thanks Tycho Brahe Johannes Kepler, working with data painstakingly collected by Tycho Brahe without the aid of a telescope, developed three laws which described the motion of the planets across the sky.

Laws of Planetary motion 1. Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.Law of Orbits 2. Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.Law of Areas 3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.The Law of Periods Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.

The Law of Orbits All planets move in elliptical orbits, with the sun at one focus. The elliptical shape of the orbit is a result of the inverse square force of gravity. inverse square forcegravity

The Law of Equal Areas A line that connects a planet to the sun sweeps out equal areas in equal times. When the planet is closer to the sun, it moves faster, sweeping through a longer path in a given time. This empirical law discovered by Kepler arises from conservation of angular momentum. conservation of angular momentum

The Law of Periods The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. This law arises from the law of gravitation. Newton first formulated the law of gravitation from Kepler's 3rd law.law of gravitation