Chapter 10 Vectors & the Geometry of Space (OLD)

Question 1

Kepler’s Laws of Planetary motion

Answer 1

1) A planet revolves around the Sun in an elliptical orbit with the Sun at one focus.
2) The line joining the Sun to a planet sweeps out equal areas in equal times.
3) The square of the period of revolution of a planet is proportional to the cube of the length of the major axis of its orbit.

Question 2

position vector of the planet (,or moon, or satellite, or comet moving around a star)

Answer 2

r =r(t)

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Question 3

velocity vector of a planet ect..

Answer 3

v = r’

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Question 4

acceleration vector

Answer 4

a = r’’

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Question 5

Second Law of motion

Answer 5

F = ma

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Question 6

Law of Gravitation

Answer 6

F = - GMm r/ r^3 = - GMm u/ r^2

r = abs(r) and u = (1/r)r <- unit vector in the direction of r
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Question 7

Combine the Second Law of motion with Law of Gravitation

Answer 7

a = - GM r/ r^3

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Question 8

Octants

Answer 8

Planes divide space into eight parts, first octant ext..