Gravitational Fields and Interactions Or I’m very attracted to you… Standards: 1e Students know the relationship between the universal law of gravitation and the effect of gravity on an object on the surface of Earth. 1m* Students know how to solve problems involving the forces between two electric charges or the forces between two masses at a distance. NGSS HS-PS2-4 : Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects. [Clarification Statement: Emphasis is on both quantitative and conceptual descriptions of gravitational and electric fields.] [Assessment Boundary: Assessment is limited to systems with two objects.]  

Gravitational Fields A mass changes the space around it so that other objects will feel a gravitational force. This change is called a gravitational force field Gravitational force field is always attractive Representations of the gravitational force field Calculating the gravitational force field g=Fg/ mtest g= G msource /d2 Units of N/kg Question: What is a gravitational field and what causes it? Which direction is the force due to a gravitational field? How are the magnitude and direction of a gravitational field represented by a field line diagram? Write the equations used to calculate the gravitational field. Activities: Discuss how no touching is needed for gravitational force to act and how we explain this with the idea of a force field around the mass. Go over idea that mass changes the space around it and we call this change a gravitational field. Mention that gravitational field is always attractive. Show several strengths of gravitational fields using force line diagrams and discuss how field always points inward because it is attractive. Point out that distance between lines is measure of strength of the field. Define g as the gravitational field variable and write the equations used to calculate it. Note that units are N/kg

Gravitational Field of Earth Gravitational Field outside Earth (apple graph) Gravitational field inside Earth Gravitational field greatest at surface of planet Gravitational field weakest in center of planet Question: Draw a graph of the gravitational field inside and outside the Earth. Where is the gravitational field the strongest? Where is it the weakest? Activities: Show apple graph and remind students of what gravitational field looks like outside of Earth. Derive the graph for gravitational field inside the Earth using the tunnel through the Earth argument. Argue for g at center to be zero which is the minimum value. Combine two graphs and point out that g=9.8 N/kg at Earth’s surface which is the maximum value

Weight Force of gravity on object from a planet Varies w/ Mass of object (~ mass) Distance from center of planet of object (1/d2) Mass of planet (~mass) Radius of planet (1/r2) Wat surface = G mplanet mbody / R planet2 Comparison Problems Question: Define weight. What quantities change the weight of an object and how? Write the equation for finding the weight of an object at the surface of a planet. Activities: Define weight as the gravitational force a planet exerts on an object. Ask what effect the source mass, test mass, planet radius and elevation above planet have on weight and write mathematical version of each on board. Derive equation for weight at surface of planet from above. Try examples of two planets with same mass but different radii and two planets with same radii but different masses. Try combination example

Check Question Two planets have the same mass. The radius of planet A is 4 times the radius of planet B. How much does an object that weighs 10 N on planet A weigh on planet B? A B

Apparent Weightlessness Not due to being too far from planet. Occurs when there is an absence of support force or an object is in free fall Gravity actually is only force acting Examples Spacecraft in orbit Falling out of an airplane or stepping off step Car or plane in Whoop de doos Elevator of Death Questions: Why do astronauts appear weightless when traveling in an orbiting space craft? What are some other examples of this phenomenon? Activity: 1) Show Video: Zero g 2) Do elevator of doom example 3) Discuss Vomit Comet and how you can get same effect by driving car over whoop de doos. 4) Discuss carnival rides free fall and what a dropped penny would do. 5) Finish by stating astronauts appear weightless because they are in free fall such that all the objects inside the cabin and the cabin itself are falling at the same rate. Thus there is no support force between these objects.

Black Holes Form from large used up stars that collapse Black hole anatomy Singularity Accretion disk Schwarzchilds radius Evidence of Black holes X rays Seen by Hubble in 1996 Also formed after big bang and were seeds for galaxies Strange properties Tidal forces Time dilation What do black holes form from? Have they been observed? What are tidal forces? Activities: Use stellar evolution poster to describe when black holes are formed. Draw diagram of black hole and discuss its anatomy. Discuss how gravitational field around black hole doesn’t change so much as it allows access to a part of the field we otherwise couldn’t get at. Discuss evidence of black holes including x ray beams, Einsteins cross and Hubble pictures. Black holes essential to galaxy formation (supermassive black holes) Take students outside and show them the cloth black hole. Roll marbles to show bending of light.

Check Question What would happen to the Earth’s orbit if the Sun suddenly became a black hole? It would decrease in diameter and be pulled into the black hole It would increase in diameter eventually escaping the black hole’s gravitational field It would remain in its same orbit with the same speed.

Tides Tides are caused by difference in gravitational pull on different parts of Earth Greater difference results in greater tides Both Sun and Moon create tides but Moon’s are greater even though Sun’s force is greater Spring and Neap tides (see next slide) Questions: What causes the tides on Earth ? Which causes larger tides the Sun or Moon? How would Earth’s tides be affected by the following; a) increasing the distance between the Earth and Moon? b) increasing the mass of the Moon? C) Increasing the diameter of the Earth?

Neap and Spring Tides Question: Draw the location of the Sun, Moon and Earth during a neap and spring tide? Which produces the highest high tides and lowest low tides?

Check Question How would doubling the following quantities affect the tides on the Earth? The mass of the Moon The diameter of the Moon The distance between the Moon and Earth The diameter of the Earth What two phases of the Moon are possible during a spring tide?