Orbits, Masses, The solar System and the Interiors of Stars

Question 1

What is Newton’s Law of gravity?

Answer 1

Mutual attraction of two masses separated by distance r: F = GMm/r^2

Question 2

What is the equation for acceleration due to gravity for a small m subject to the gravity of M at its surface radius R?

Answer 2

g = GM/R^2

Question 3

What is the value of the gravitational constant G?

Answer 3

G = 6.67*10^-11 N m^2 kg^-2

Question 4

How does an orbit work?

Answer 4

A mass orbiting another mass needs to find equilibrium between the gravitational attraction and the centripetal acceleration to be in orbit.

Question 5

How do you derive Keplers third Law?

Answer 5

-v = ΩR, where Ω = 2pi/P
Fc = mv^2/R
Fg = GMm/R^2
Set the two force equations equal to eachother and then substitute in velocity. Then rearrange.

Question 6

What is the finding of Kepler’s Third Law?

Answer 6

P^2 ∝ R^3, where P is the period.

Question 7

What is the equation for Kepler’s law in the general case of a binary system?

Answer 7

Ω^2 = 4pi^2/P^2 = G(m1+m2)/R^3