Escape velocity and formulas for circular orbits

  • #1
In my class, we developed a list of formulas for circular orbits. One of them is E/m=1/2v2-GM/r=constant. To derive escape velocity we find for what v does E=0. But an orbit of this nature is certainly not circular! How can we apply the formula?
 

Answers and Replies

  • #2
chroot
Staff Emeritus
Science Advisor
Gold Member
10,226
34
Bound orbits are those with E < 0.

- Warren
 
  • #3
Janus
Staff Emeritus
Science Advisor
Insights Author
Gold Member
3,555
1,325
The formula given is true for all orbits; whether they be circular, eliptical, parabolic or hyperbolic.

As Warren pointed out, circular or eliptical orbits will have E<0

A parabolic orbit (the one followed by an object traveling exactly at escape velocity) E=0

For E > 0, you get a hyperbolic orbit.

One thing about circular orbits:

v= [squ](GM/r) at all points. if you substitute this for v in the formula you have it reduces to

E=-GMm/2r

Now, this turns out to be also true for eliptcal orbits if you substitute the semi-major axis(a) for r. (the semi-major axis is half of the longest dimension of the ellipse. It is also the Average length of the radius vector over the course of an orbit. )

This gives

E = -GMm/2a
 

Related Threads on Escape velocity and formulas for circular orbits

  • Last Post
Replies
3
Views
22K
Replies
2
Views
3K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
1
Views
749
  • Last Post
Replies
3
Views
744
  • Last Post
Replies
2
Views
9K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
13
Views
5K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
2K
Top