Newton's Law of Universal Gravitation

1. Define the term gravity field.

(gravity field) =	(gravity force)
	(unit of mass)

2. Explain why gravity field is a vector.

3. Define Newton's Law of Universal Gravitation in mathematical form and evaluate the nature of the forces involved.

mathematical form: F = (G∙M∙m) / r²

M and m represent 2 point sources of mass that are being pull together by an action/reaction pair of gravity forces. While the forces are opposite in direction, each has a magnitude of F as calculated above even though one of the masses could be much larger than the other.

4. Explain the assumptions and limitations of Newton's Law of Universal Gravitation

   assumes planets act as point sources of mass. The variable r in the equation is the distance between the center of mass of the 2 masses.

only works at or above the surface of a planet. If the equation worked inside the planet, then at the center, the gravitational attraction force would be infinity. However, at the center the force = 0.

5. Draw and compare the gravity fields for 2 different mathematical models using rays.

Flat Earth (useful near the surface) : F = mg

Spherical planet: F = (GMm) / r²

6. Describe the gravity field inside a hollow planet. g = zero

Applications of Newton's Law of Universal Gravitation

7. Solve inverse square law type problems using Newton's Law of Universal Gravitation.

8. Combine F = mg with the Universal Gravitation Equation to find an expression for g.

   Formative assessment: Evaluate the effects on g for a planet if the mass and/or radius are altered by various factors.

   radius = 6.371 x 10⁶meters

   mass = 5.9736 x 10²⁴ kg

   G = 6.754 x 10^-11 m³/kg/s²

    

Homefun (formative/summative assessment): Read sections 7.1

Formative Assessment: Physics Investigation

Light intensity = (amount of light) / (unit of area)

Note: the division operator or / can be verbalized as "per". Hence, Light intensity is the amount of light per unit of area.

Graphing a Planet's Gravity Force

10. Graph the gravity force vs. distance from the center of a planet assuming that a tunnel exists that would allow an object to pass from one side of a planet to the other through the center of the Earth.

11. Describe the motion that would occur if an object were dropped in the tunnel, assuming no air resistance and explain how theoretically this would be an incredibly good form of transportation.

     

Homefun (formative/summative assessment): Read section 7.2, do Section Review Problems 7, 11 p. 178.

Orbits of Satellites

12. Calculate the weight force acting on an object in orbit. F = (GMm)/r²

    Formative assessment: What is the weight of a 150 lb object 1.6 x 10⁶meters or roughly 1000 miles above the surface of the Earth?

13. Explain why a person in orbit actually has a significant amount of weight even though they feel weightless.

14. Derive an expression for the velocity required to maintain a given circular orbit using the following models:

Starting Information	Final Product
F = ma F = (GMm) / r2 a = v2/ r	v = (GM/r)1/2

 

15. Derive an expression for the period of a circular orbit given the orbital velocity and radius from the center of a planet. Use the following:

S = d / t

period: (the time it takes to complete 1 orbit) = T

distance traveled in one orbit: (the circumference) = 2πr

Final Product

T = 2π[ r3/ (GM) ]1/2

 

16. Define what a geostationary orbit is and why it is of significant usefulness to humans.

17. Neglecting air resistance, explain why heavier masses do not fall at a greater rate of acceleration than lighter weight masses and why the mass of an orbiting object does not affect the conditions required for orbit.

Homefun (formative/summative assessment): problems 15, 17 p. 185; 31, 33, 37, 51, 71 p. 190 to 193

Review of Objectives 1- 13 (1-3 days)

Formative Assessments:

1. Work review problems at the board

2. Work practice problems.

Metacognition Problem Solving Question: Can I still work the problems done in class, several hours or days later? Some amount of repetition on the exact same problems is necessary to lock in learning. It is often better to thoroughly understand a single example of a problem type than to work example after example understanding none of them completely.

Relevance: Good test preparation is essential to performance in physics class.

Homefun (formative/summative assessment): problems 81, 89, 91, 59 pages 193-194; problems turn in on the day stapled to the back of the test.

Summative Assessment: Unit exam objectives 1-16