Astronomy 1010Fall_2015Day-16

Planetary Astronomy

Kill time

Course Announcements• Dark Sky nights – Mon. 10/5 & Wed. 10/7 starting at

7:30pm – at the Observatory.

• Exam-2 will be Friday, Oct. 9

• SW-chapter 4 posted: due Mon. Oct. 5• First Thursday Art Walk 5-8pm tomorrow; downtown

Definitions & Terms -1• Tide: (1) A laundry detergent

• (2) A gravitational interaction which goes as d3

Lecture – TutorialNewton’s Law of Gravity: pg 29

Work with a partner!Read the instructions and questions carefully.Discuss the concepts and your answers with one

another.Come to a consensus answer you both agree on.If you get stuck or are not sure of your answer,

ask another group.If you get really stuck or don’t understand what

the Lecture Tutorial is asking, ask one of us for help.

i-Clicker Question

Renaissance Astronomy: Gravity Calculations 1

PROCESS OF SCIENCEPROCESS OF SCIENCE For a theory to be

“scientific”, it must be testable.

Old theories that are disproven lead to greater insight.

Newton’s Law and Gravitation

• All my favorite Projectiles behave like this!!!

Force

Velocity

Acceleration

Kepler’s laws of orbits and Newton’s laws of motion and gravity are only the beginning.

Gravity is very important for shaping objects and orbits.

Internal forces Tides Orbital resonances

The gravitational force results in an acceleration.

All objects on Earth fall with the same acceleration known as g.

g = 9.8 m/s2

weightF m g

Gravity is an attractive force between any two objects with mass, acting along the line between them.

It depends on the objects’ masses. It depends on the distance between them.

G is the universal gravitational constant. The m terms are the two masses. More mass = more force.

The distance between the objects is r. A greater r = smaller force. Gravity is governed by an inverse square

law.

i-Clicker Question

Renaissance Astronomy: Gravity Calculations 4

In the Earth-Moon system, the gravitational force of Earth on the Moon is equal to the gravitational force of the Moon on Earth.

The accelerations are different! Remember Newton’s second law: F = m a. The more massive object will have a smaller

acceleration, while the less massive object will have a larger acceleration.

It is the same in the Sun-Earth system.

The gravitational interaction of three bodies leads to Lagrangian equilibrium points.

These are special orbital resonances where the object at that point orbits in lockstep.

SOHO is near L1.

CONNECTIONS 4.2

Orbits describe one body falling around another.

The less massive object is a satellite of the more massive object.

The two bodies orbit a common center of mass.

For a much smaller satellite, the center of mass is inside the more massive body.

An astronaut inside an orbiting space shuttle will experience free fall because he is falling around Earth at the same rate as the shuttle.

He is not weightless.

Gravity provides the centripetal force that holds a satellite in its orbit.

Uniform circular motion: moving on a circular pathat constant speed.

Still experiencing an acceleration since the direction is constantly changing.

Planets in real-world scenarios move on elliptical orbits.

The gravitational force changes both the direction and the speed of the planet as it moves in its orbit.

Results in Kepler’s law of equal areas.

Circles and ellipses are bound orbits. Objects with higher orbital speeds can

escape bound orbits to be in unbound orbits. Parabolas and hyperbolas are examples.

Newton derived Kepler’s laws from his law of gravity.

Physical laws explain Kepler’s empirical results:

Distant planets orbit more slowly; the harmonic law and the law of equal areas result.

Newton’s laws were tested by Kepler’s observations.

i-Clicker Question

Renaissance Astronomy: Graph Orbital VelocitiesRenaissance Astronomy: Graph Kepler’s 3rd Law

The velocity of an object traveling in a circular orbit can be found by equating the gravitational force and the resulting centripetal force.

This yields: You can solve for the period by noting that

This yields Kepler’s third law:

MATH TOOLS 4.2

Tides are a consequence of gravity.

Something closer to an object experiences a stronger gravitational pull than something else farther away.

The centers of Earth and the Moon orbit like point masses.

Parts of Earth are closer to the Moon than other parts.

This produces a stretch on the Earth, called a tide.

Tides cause bulges to appear on either side.

Earth’s oceans flow in response to the tidal forces.

The oceans have a tidal bulge: They are elongated in a direction that is nearly pointed at the Moon.

Earth rotates under the tidal bulge.

We get two high and two low tides each day.

The behavior is complicated by Earth’s landmasses and solar tides.

Tides can affect the solid part of Earth, too.

A gravitational pull can stretch and deform a solid body.

Results in friction, which generates heat. Friction also opposes the rotation of Earth,

causing Earth to very gradually slow its rotation.

Days lengthen by about 0.0015 seconds every century.