Physics Lesson 12/1

Physics Lesson 12/1

Orbits of Planets and Satellites

Open Ended

Journal - Chop Wood Carry Water

Classroom Discussion

Could you theoretically shoot a cannon ball around the world?

Orbits of Planets and Satellites

• The planet Uranus was discovered in 1781

• By 1830, it was clear that the law of gravitation didn't correctly predict its orbit

• Any guesses as to why the law didn't work on Uranus?

Orbits of Planets and Satellites

• Two astronomers proposed that Uranus was being attracted by the Sun (Normal Gravity) and and by an undiscovered planet.

• In 1845, they calculated the orbit of such a planet

• One year later, astronomers at the Berlin Observatory found the planet now called Neptune.

• How is it possible for planets such as Neptune and Uranus to stay in orbit around the Sun?

Newton and Cannonballs

• Back to our opening question...

• Newton used a drawing similar to the one on the right to illustrate a "thought experiment" on the motion of satellites.

Newton and Cannonballs

• Imagine a cannon perched high on a mountain, firing a cannonball horizontally with a given horizontal speed.

• The cannonball is a projectile, and its motion has both vertical and horizontal components.

Newton and Cannonballs

• Like all projectiles on Earth, the cannonball would follow a parabolic projectile and fall to Earth. (Trajectory A)

• But what if we increased the horizontal velocity of the cannonball?

Newton and Cannonballs

• Then we end up with something like Trajectory B. It still will fall to Earth, travelling in a parabolic Earth, yet it travels farther.

• Now, what if we use an EXTREMELY powerful cannon, the cannonball could make it all the way around the Earth (Trajecxtory C)

Newton and Cannonballs

• It would fall toward Earth at the same rate that Earth's surface curves away.

• In other words, the curvature of the projectile would curvature of the Earth

The Cannonball would be in

ORBIT!

The problem with Newton and Cannonballs

• Newton's "thought experiment" ignored air resistance.

• For the cannonball to be free of air resistance it would have to be more than 150 km above the Earth's surface.

• For comparison, Mount Everest is 8.85 km in height.

• If a cannonball or any other object or satellite was launched at this height, it could orbit the Earthj.

A satellites speed.

• A satellite in an orbit that is always the same height above Earth moves in uniform circular motion.

• Solving for the speed of a satellite in circular orbit about Earth (v) yields the following..

•  $v=\sqrt{\frac{Gm_E}{r}}$  

A satellite's orbital period.

• A satellite's orbit around teh Earth is similar to a planet's orbit around the Sun. The equation is very similar to the equation we learned yesterday with a minor modification.

•  $T=2\pi\sqrt{\frac{r^3}{Gm_E}}$  

Open Ended

Assume that a satellite orbits Earth 225 km above its surface. Given that the mass of Earth is 5.97 X 10²⁴ kg and the radius of Earth is 6.38 X 10⁶ m, what are the satellite's orbital speed and period?

Practice Problems

Open Ended

Exit Ticket - What is meant by the Period of a Satellite?