ChemPhys 173/273

Unit 9: Circular Motion and Gravitation

Problem Set B

 

Overview:

Problem Set B targets your ability to use the Newton's laws of universal gravitation and the other equations derived from it in order to analyze the motion of satellites and celestial objects. A number of concepts and mathematical formulas will be of importance in your completion of this set. These concepts and formulas are described below.

 

 

 

 

 

 

Summary of Mathematical Formulas

One difficulty a student may encounter in this problem set is the confusion as to which formula to use. The table below provides a useful summary of the formulas pertaining to circular motion and satellite motion. In the table, many of the formulas were derived from other equations. Thus, there will often be more than one means of determining an unknown quantity. In approaching these problems, it is suggested that you practice the usual habits of an effective problem-solver; identify known and unknown quantities in the form of the symbols of physics formulas, plot out a strategy for using the knowns to solve for the unknown, and then finally perform the necessary algebraic steps required for the solution.

 

To calculate ...

... use the equation(s):

Speed

(v)

v = 2 • pi • R / T

v = SQRT (G • Mcentral / R) for satellites only

Acceleration

(a)

a = v2 / R or a = Fnet / m

a = g = G • Mcentral / d2 for satellites only

Net force

(Fnet)

Fnet = m • aorFnet = m • v2 / R

Fnet = Fgrav = G • msat • Mcentral / d2 for satellites only

Period

(T)

T = 2 • pi • R / v

T2 = 4 • pi2 / (G • Mcentral ) • R3 for satellites only

 

Additional Readings/Study Aids:

The following pages from The Physics Classroom tutorial may serve to be useful to understanding Newtons law of universal gravitation and the mathematics of satellite motion.

Speed and Velocity | Centripetal Acceleration | Mathematics of Circular Motion

Law of Universal Gravitation | Value of g | Kepler's Three Laws | Mathematics of Satellite Motion

  

View Sample Problem Set.

 

Problem

Description

Audio Link
1

Routine calculation of the gravitational force between two objects of known mass and separation distance.

2

Use of Newton's law of gravitation as a guide to thinking about how distance of separation effects the gravitational force.

3

Routine calculation of the gravitational force between two objects of known mass and separation distance.

4

Routine calculation of the gravitational force between two objects of known mass and separation distance.

5

Determination of the net gravitational force based upon the calculation of the two individual gravitational forces.

6

Complex analysis to determine the altitude above Earth at which the acceleration of gravity is some specified value.

7

Routine calculation of the acceleration of gravity at a given location about a planet.

8

Routine calculation of the acceleration of gravity at a given location about a planet.

9

Determination of the acceleration of gravity at a specified altitude above the Moon's surface.

10

Referring to the previous problem; determination of the speed of a satellite at the specified altitude above the Moon's surface.

11

Referring to the previous problem; determination of the orbital period of the satellite.

12

Determination of the acceleration of gravity at a specified altitude above the Earth's surface.

13

Determination of the orbital period of the satellite at a given altitude above the Earth's surface.

14

Referring to the previous problem;

15

Referring to the previous problem; determination of the orbital period of the satellite.

16

Complex analysis to determine the location between two celestial bodies of known mass and separation distance at which the net gravitational force would be 0 N.

17

Determination of the mass of a planet from knowledge of the orbital radius and period of one of its moons.

18

Determination of the acceleration of gravity at a specified altitude above the Moon's surface.

19

Determination of the orbital period of a satellite at a specified altitude above the surface of Mars.

20

Determination of the orbital speed of a satellite at a specified altitude above the surface of the Earth.

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