Calculus Volume 3 · free preview
Motion in Space
Planetary and projectile motion follow from Newton's law as vector differential equations, with Kepler's laws emerging for inverse-square gravity and the tangential-normal decomposition separating speed changes from steering.
1. Newton's second law in vector form
Newton's second law in vector form
2. Planetary motion and Kepler's laws
Planetary motion and Kepler's laws
3. Tangential and normal components
Tangential and normal components
4. The two-body reduction
The two-body reduction
5. Central force consequence
A central force, pointing always toward a fixed center, conserves which quantity?
6. Tangential component meaning
The tangential component a_T of acceleration measures what?
7. Normal component formula
The normal component a_N equals which expression?
8. Kepler first law content
Kepler's first law states that planets orbit in which conic sections with the sun at a focus?
9. Projectile horizontal motion
A projectile launched in a uniform gravitational field experiences which horizontal motion?
10. Projectile vertical acceleration
The projectile's acceleration vector is (0, 0, -g). As a number, what is its x component? Answer with a number.
11. Angular momentum formula
Angular momentum L equals r crossed with which other vector? Answer like m v.
12. Centripetal naming
The normal acceleration kappa |v|^2 is also called centripetal, from Latin for center-seeking. As a single word, what is it? Answer in lowercase.
13. Why central gives planar
A central force produces planar motion because the conserved quantity keeps the position and velocity in which configuration?
14. Equal areas law
Kepler's second law, equal areas in equal times, restates which quantity's conservation? Answer with two words.
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