2.22.2ORBITAL MOTION AND ORBITAL MOTION AND

TIDESTIDES

2.22.2ORBITAL MOTION AND ORBITAL MOTION AND

TIDESTIDES

In order to stay on a closed orbit, an object has to be within a certain range of velocities:

Too slow Object falls back down to Earth

Too fast Object escapes Earth’s gravity

Orbital Motion

http://hal.physast.uga.edu/~rls/1020/ch5/cannonball.swf

Orbital Velocity

An object orbiting Earth is actually falling (being accelerated) toward Earth’s center.Continuously misses Earth

due to its orbital velocity.

To follow a circular orbit, the object must move at circular velocity.

G = gravitational constant; 6.67 x 10-11 m3/kg•s2

M = mass of the central body in question

r = radius of the orbit (m)

Circular Velocity Example How fast does the moon travel in its orbit?

Hint: Earth’s mass is 5.98 x 1024 kg, and the radius of the moon’s orbit is 3.84 x 108 m.

GEOSYNCHRONOUS ORBITS

Escape Velocity

The velocity required to escape from the surface of an astronomical body is known as the escape velocity.

G = gravitational constant; 6.67 x 10-11 m3/kg•s2

M = mass of the central body in question

r = radius of the orbit (m)

Escape Velocity Example Find the escape velocity from Earth.

Newton’s Version of Kepler’s 3rd Law

The equation for circular velocity:

The circular velocity of a planet is simply the circumference of its orbit divided by the orbital period:

If you substitute this for V in the first equation and solve for P2, you will get:

NVK3L Powerful formula in

astronomy because it allows us to calculate the masses of bodies by observing orbital motion.For example, you observe a

moon orbiting a planet and can measure the size of its orbit, r, and its orbital period, P.

You can now use this formula to solve for M, the total mass of the system.

There is no other way to find the masses of objects in the universe stars, galaxies, other planets.

G = gravitational constant; 6.67 x 10-11 m3/kg•s2

M = mass of the total system (kg)

r = radius of the orbit (m)

NVK3L Example Planet Cooper has a radius of 6840 km.

and a mass of 5.21 x 1025 kg. What is the orbital period of a satellite orbiting just above this planet’s surface?

Tides and Tidal Forces Earth attracts the moon, and the moon attracts Earth.

Tides are caused by small differences in gravitational forces. Oceans respond by flowing into a bulge of water on the side of Earth

facing the moon. Also a bulge on the side of Earth facing away from the moon since the

moon pulls more strongly on Earth’s center than the far side of the moon.

Tides and Tidal Forces You might wonder … If the moon and

Earth accelerate toward each other, why don’t they smash together?They are orbiting around a common center

of mass!

Spring Tides Gravity is universal, so the Sun also produces tides on Earth.

Twice a month, at new moon and full moon, the moon and Sun produce tidal bulges that add together and produce extreme tidal changes. High tide exceptionally high; Low tide exceptionally low.

These are called spring tides. “Spring” refers to the rapid welling up of water.

Neap Tides At 1st and 3rd quarter moons, the Sun and moon pull at

right angles to each other, and the Sun’s tides cancel out some of the moon’s tides.

These less-extreme tides are called neap tides. “Neap” means lacking power to advance.