T1: 9. Einstein's Equations

Question 1

In Newtonian gravity (NG), give the gravitational force on a test mass m.

Answer 1

F = -GMm/r^2 e_r

With F and e_r as vectors

Question 2

In the NG eq. which direction between masses does e_r point?

Answer 2

From M to m.

Question 3

Define a conservative force

Answer 3

A force for which the work done moving an object between two points is independent of the path taken.

Question 4

In NG, give the gravitational force knowing it is a conservative force.

Answer 4

F = -m∇ϕ

With F and ∇ as vectors, and ϕ some potential.

Question 5

In NG, writing the gravitational force prop to ∇ϕ, give ϕ.

Answer 5

ϕ = -GM/r

Question 6

How does the energy of a test mass change with proximity to source mass M

Answer 6

Energy gets smaller (ϕ more negative) as it gets closer to the source.

Question 7

How does the energy of a test mass change with proximity to source mass M

Answer 7

Energy gets smaller (ϕ more negative) as it gets closer to the source.