1. Gravity, Orbits & Tides

2. The Study of Gravity
Astronomers study gravity to describe and understand the motions of objects in space.
Isaac Newton
Gets credit for describing gravity
Could not explain what caused gravity
Einstein proposed that gravity is a curvature of space and time
What is gravity? Why does it exist?

3. Isaac Newton: A New Era of Science
Mathematics as a tool for understanding the physical world.

4. Isaac Newton ( )
Building on the results of Galileo and Kepler
Applied physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler
Major achievements:
Invented Calculus to solve mathematical problems related to motion
Defined the three laws of motion
Defined the universal law of gravitation

5. Velocity and Acceleration
Acceleration (a) is the change of a body’s velocity (v) with time (t): a
a = Dv/Dt
Velocity and acceleration are directed quantities (vectors)! v
Different cases of acceleration:
Acceleration in the conventional sense (i.e. increasing speed)
Deceleration (i.e. decreasing speed)
Change of the direction of motion (e.g., in circular motion)

6. Acceleration of Gravity
independent of mass
All objects of the same SHAPE fall at the same rate
Wood ball
Iron ball

7. Newton’s 1st Law of Motion
Unless acted on by an outside force,
an object that is not moving will not move
an object that is moving will continue to move with the same speed and direction
An astronaut floating in space will continue to float forever in a straight line unless some external force accelerates him or her.

8. Newton’s 2nd Law of Motion
The acceleration, a, of an object is
inversely proportional to its mass, m
in the same direction and directly proportional to the net force, F
a = F/m  F = m a

9. Newton’s 3rd Law of Motion
To every action, there is an equal and opposite reaction.
M = 70 kg
V = ?
The same force that is accelerating the boy forward, is accelerating the skateboard backward.
m = 1 kg
v = 7 m/s
V = 0.1 m/s

10. The Universal Law of Gravity
Any two bodies, M and m, are attracted to each other through gravitation. The gravitational force, F, is
Proportional to the product of the masses, M x m
Inversely proportional to the square of their distance:
G is the Universal Constant of Gravity
G = × m3/kgs2
F = G Mm d2

11. Understanding Orbital Motion
The Universal Law of Gravity describes the orbital motion:
According to the 1st law, the moon would move in a straight line with constant velocity, v.
Earth and moon attract each other through gravitational force, F.
The Earth has more mass than the moon so the moon’s effect on Earth is small. This shifts the center of the gravitational force closer to the Earth
Earth’s gravitational force, F, constantly accelerates the moon towards Earth
This acceleration is constantly changing the moon’s direction of motion, Δv, holding it on its almost circular orbit
Earth
Moon v v’ Dv F

12. Center of Mass

13. Orbital Motion (2)
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

14. Click on the link to see how this works:
Newton’s Cannon
Click on the link to see how this works:

15. Geosynchronous Orbits
Orbital Motion (3)
Geosynchronous Orbits

16. Geosynchronous Orbit

17. Kepler’s 1st and 2nd Laws
The orbit of every planet is an ellipse with the Sun at one of the two foci.
A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

18. Kepler’s 3rd Law … Explained by Newton
Kepler’s 3rd Law states that for any orbiting body,
the square of the Period of Revolution in years =
the cube of the average distance measured in AU
Py2 = dAU3
Newton described the “Centripetal Force”, a force that balances the orbiting objects circular motion.

19. Tides on Earth
Tidal Force = the difference in gravity from one side of a body to the other that is exerted by a 2nd object.
The Moon’s tidal force on Earth
causes the oceans facing the Moon to bulge out toward it
the oceans on the opposite side of the Earth to bulge out away from the Moon.
These varying ocean levels are called the tides.

20. Tides on Earth
The Sun also causes tides on the Earth, but they are smaller than the Lunar tides because the Sun is further from the Earth than the Moon.
When the Moon and Sun are aligned, their tidal forces combine, and the resulting tides are largest.
Spring Tides - Largest
Neap Tides - Smallest

22. Tidal Friction
The Earth is constantly rotating, pulling the tidal ocean bulge out of alignment. As a result, the water is continually moving in the opposite direction of the Earth’s rotation.

23. Tidal Friction The movement of the water on Earth has two effects:
It slows down the Earth’s rotation (few milliseconds per century).
When dinosaurs roamed the Earth, a day was 22 hours long.
Eventually, the Earth will rotate once in the same time the Moon orbits once. So the Earth and Moon will always have the same faces toward each other.

24. Tidal Friction The movement of the water on Earth has two effects:
It pulls the Moon along a bit faster, slinging it out further from the Earth (about 4 cm per year).
In the distant past, the Moon was much closer to the Earth.

25. Tides on Moon Lunar tidal forces are slowing the Earth’s rotation
it will keep the same face toward the Moon
Earth is about 80 times more massive than the Moon
its tidal force is 80 times greater.
Tidal friction of flowing rocks (lava) has already locked the Moon to the Earth.
THIS is why the Moon always keeps the same side facing the Earth.
Remember…from the Earth, we never see the far side of the Moon.

26. Tidal Patterns Semi-Diurnal: 2 high waters and 2 low waters per day
Diurnal: 1 high water and 1 low water per day
Mixed: A combination of Semi-Diurnal and Diurnal patterns

27. Tidal Patterns Tides are described by TIME and AMPLITUDE
Variations are caused by
Alignment of Sun and Moon
Patterns of tides in the deep ocean
Harmonics of tidal movements
Shape of Coastline and bathymetry

28. Size of Tidal Variations