Gravitational Fields

Question 1

Newton’s law of Gravitation

Answer 1

F = Ma Gb
F = Mb Ga
F= kr^2
We have to put all these together. From the first and second equations, we know that Gb must have Mb in it, and Ga must have Ma in it. We know gravitational fields are a consequence of mass. Therefore:
F(w) = m(a) m(b) B r^2
Rename constant to G for gravitation, this leads us to Newton’s law of Gravitation:
G m(a) m(b)
F(w) = - —————
r^2
The minus sign is there to signify that it is an attractive force.

Question 2

Gravitational constant

Answer 2

G = 6.67x10-11 m^3 kg^-1 s^-2

Question 3

Derivation of Gravitation units

Answer 3

F(w) = Gm(a) m(b) / r^2
so
G = F(w) r^2 / m(a) m(b)
Therefore:
G = Nm^2 / kg kg
[G] = Nm^2 kg^-2
[G] = kgms^-2 m^2 kg^-2
[G] = s^-2 m^3 kg^-1
[G] = m^3 kg^-1 s^-2

Question 4

Gravitational Potential definition

Answer 4

The GPE per unit mass

Question 5

Gravitational Field Strength

Answer 5

Force per unit mass

Question 6

Gravitational Potential Equations

Answer 6

GPE = G m(a) m(b) / r
V = Gm(b) / r