Conversion of spherical harmonics (Kaula, 3.3)I2.2a We want to express the terms in the expansion in Kepler variables:. C.C.Tscherning, 2005-11-03.

Slides:

Advertisements

Similar presentations

Goal When you have finished this presentation you should understand:

Advertisements

Fig. 4-1, p Fig. 4-2, p. 109 Fig. 4-3, p. 110.

Slide 1Fig. 2.1a, p.25. Slide 2Fig. 2.1b, p.25 Slide 3Table 2.1, p.25.

General equations of motion (Kaula 3.2)I2.1a. C.C.Tscherning,

Decimal Conversion Conversion of fractions into decimal value involves long division. Remember the numerator goes under the bracket, and the denominator.

Slide 1Fig. 22.1, p.669. Slide 2Fig. 22.3, p.670.

Slide 1Fig. 17.1, p.513. Slide 2Table 17.1, p.514.

Slide 1Fig. 11.1, p.337. Slide 2Fig. 11.2, p.338.

Slide 1Fig. 19.1, p Slide 2Fig. 19.2, p. 583.

Slide 1Fig. 21.1, p.641. Slide 2Fig. 21.2, p.642.

Slide 1Fig. 10.1, p.293. Slide 2Fig. 10.1a, p.293.

P.464. Table 13-1, p.465 Fig. 13-1, p.466 Fig. 13-2, p.467.

Satellite geodesy. Basic concepts. I1.1a = geocentric latitude φ = geodetic latitude r = radial distance, h = ellipsoidal height a = semi-major axis, b.

Fig. 11-1, p p. 360 Fig. 11-2, p. 361 Fig. 11-3, p. 361.

Conversion of spherical harmonics (Kaula, 3.3)I2.2a We want to express the terms in the expansion in Kepler variables:. C.C.Tscherning,

Table 6-1, p Fig. 6-1, p. 162 p. 163 Fig. 6-2, p. 164.

ARCGICE WP 2.1 Leader: DSPC Make new geoid of afrctic region based on GRACE C.C.Tscherning, University of Copenhagen,

From CIS to CTS We must transform from Conventional Inertial System to Conventional Terrestrial System using siderial time, θ: Rotation Matrix C.C.Tscherning,

Orbit Determination (Seeber, 3.3), sat05_42.ppt,

Satellite geodesy: Kepler orbits, Kaula Ch. 2+3.I1.2a Basic equation: Acceleration Connects potential, V, and geometry. (We disregard disturbing forces.

Figure 1.1 The observer in the truck sees the ball move in a vertical path when thrown upward. (b) The Earth observer views the path of the ball as a parabola.

1 times table 2 times table 3 times table 4 times table 5 times table

Problem of the Day Problem of the Day Division next.

12.1 – Simplifying Rational Expressions A rational expression is a quotient of polynomials. For any value or values of the variable that make the denominator.

Measurement (Ch 3) Handout #2 answers

Combinational Circuit – Arithmetic Circuit

Chapter 5: Operations with Fractions 5.2 Fractions & Decimals.

6.1 Factoring Polynomials Goal: To factor out a common factor of a polynomial.

Chapter 5 Z Transform. 2/45  Z transform –Representation, analysis, and design of discrete signal –Similar to Laplace transform –Conversion of digital.

Lesson 1.7 Dividing Integers Standards: NS 1.2 and AF 2.1 Objectives: Dividing Integers Evaluate variable expressions.

Table of Contents A Quadratic Equation is an equation that can be written in the form Solving Quadratic Equations – Factoring Method Solving quadratic.

Objective The student will be able to: recognize and use the commutative and associative properties and the properties of equality.

Variables and Algebraic Expressions 1-3. Vocabulary Variable- a letter represents a number that can vary. Constant- a number that does not change. Algebraic.

Quantitative Values in Chemistry (Math!!) Scientific Notation Used for writing very small or very large numbers. Written as the coefficient multiplied.

The Ratio Test: Let Section 10.5 – The Ratio and Root Tests be a positive series and.

IB Computer Science – Logic

Table of Contents Solving Polynomial Equations – Factoring Method A special property is needed to solve polynomial equations by the method of factoring.

1. x = x = x = x = x = x = x = x = x = x = x = x = 4 Story Problems.

Exponents Exponents mean repeated multiplication 2 3 = 2  2  2 Base Exponent Power.

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

Tables Learning Support

Conjugate Pairs Theorem Every complex polynomial function of degree n  1 has exactly n complex zeros, some of which may repeat. 1) A polynomial function.

Simplify Radical Expressions Using Properties of Radicals.

Products and Factors of Polynomials (part 2 of 2) Section 440 beginning on page 442.

EXPONENTS Basic terminology Substitution and evaluating Laws of Exponents Multiplication Properties Product of powers Power to a power Power of a product.

02CO, p. 29. Fig. 2.1, p. 30 Fig. 2.2, p. 31 Fig. 2.3, p. 31.

Fig. 6-CO, p p. 185a p. 185b p. 185c p. 185d.

5.1 Properties of Exponents

Decimal Conversion Conversion of fractions into decimal value involves long division. Remember the numerator goes under the bracket, and the denominator.

Multiplying Integers.

Tonight’s Homework: Finish Review Sheet and Study!!!! Warm UP

Unit 0.5 Warm Up #1 How many sig figs are there in the following?

בשואה הגיעה ההיסטוריה היהודית לסופה מה מתחיל כעת עדיין איננו יודעים

Divisibility Rules.

Divisibility Rules.

Fig. 6-CO, p. 211.

Multiply and divide Expressions

3 times tables.

6 times tables.

Lesson 3 Negative exponents

BETONLINEBETONLINE A·+A·+

COURSE 3 LESSON 3-3 Understanding Slope

FRACTIONS & DECIMALS.

Pole Position Student Points Time

Lesson 3.3 Writing functions.

Presentation transcript:

Conversion of spherical harmonics (Kaula, 3.3)I2.2a We want to express the terms in the expansion in Kepler variables:. C.C.Tscherning,

Kaula (3.48, 49) C.C.Tscherning,

Kaula (3.51) C.C.Tscherning,

Kaula (3.53, 54) C.C.Tscherning,

Kaula (3.55,56), fig. 4. C.C.Tscherning,

Kaula (3.57). C.C.Tscherning,

Development of P nm C.C.Tscherning,

Kaula (3.58,59). C.C.Tscherning,

Kaula (3.60,). C.C.Tscherning,

Kaula (3.61, 62). C.C.Tscherning,

Kaula Table 1. C.C.Tscherning,

Kaula C.C.Tscherning,

Kaula 3.72, C.C.Tscherning,

Kaula C.C.Tscherning,

Kaula With C 20 = , e=0.001, a=1.2a e C.C.Tscherning,

Kaula C.C.Tscherning,

Resonance, Kaula 3.6 Terms become zero, or ”infinite” by division with zero. C.C.Tscherning,

Orbit with repeating ground track Orbit which gives resonance with specific term(s) Orbit which is sun-syncroneous Orbit which enables close ”encounter” with an object, such as the poles. Applications C.C.Tscherning,