Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

Question #b5ee5

1 Answer

Oct 3, 2016

see below

Explanation:

Because it is in Newtonian Equilibrium, we can say that:

$\frac{m v^{2}}{r} = \frac{G M m}{r^{2}}$ $(m v^2)/ r = (GMm)/(r^2)$

... thus balancing centrifugal and centripetal forces

$\Rightarrow v = \sqrt{\frac{G M}{r}}$ $implies v = sqrt ( (GM)/(r) )$ , which is "speed"

In terms of aceleration:

$a_{r} = - \frac{v^{2}}{r} = - \frac{G M m}{r^{2}}$ $a_r = - (v^2)/ r = - (GMm)/(r^2)$ ,

Related questions

See all questions in Introduction to Vectors

Impact of this question

1567 views around the world

You can reuse this answer
Creative Commons License