*Gravitational And Planetary Rotation

Question 0

See the analytical geometry section of your calculus notes

Answer 0

Do it now

Question 1

Kepler’s first law

Answer 1

Planetary motion takes the form…
1=(x/a)^2+(y/b)^2
Always an Ellipse

Question 2

Gravitational fields

Answer 2

Negative gradient of gravitational potential

G=-∇P

Question 3

See the section on vector fields and vector calculus

Answer 3

Do it now

Question 4

Gravitational force between two objects

Answer 4

F=G(m1*m2)/r^2

Question 5

Universal gravitational constant

Answer 5

G=6.67x10^-11

Question 6

Keplers second law

Answer 6

The area inside the ellipse, the net space between the initial (a) and final (b) distances from the smaller to the larger mass, is equal to all other areas measured in the same length of time, regardless of the larger masses position within the ellipse.
Meaning the magnitude of the vector function at the final time (t) can be calculated through √(a^2sin^2(t)+b^2cos^2(t)). Integral of this is arc length. Derivative (acceleration) is proportional to the radius (r).

Question 7

Kepler’s third law

Answer 7

Period of orbit (T) squared over average distance (d) cubed is known as the ‘orbital ratio’
Equal to those of similar average vectors
(T1^2)/(R1^3)≈(T2^2)/(R2^3)

Question 8

Gravitational energy (uniform)

Answer 8

Ug=Fg(m)*r

Question 9

Gravitational energy (non-uniform)

Answer 9

Ug=(Gm1m2)/d