Hi!
I was wondering why planets at Perihelion travel faster than planets at Aphelion?
Is it incorrect to use the equation for orbital velocity (i.e. tangential velocity of an orbit in CIRCULAR motion) to explain why?
Mathematically:
V(orbital) = √(GM/R)
I know it sounds silly asI'm trying to explain speeds for objects in elliptical orbits, however it is the only justification that springs to mind.
Please help!
Thanks
Elliptical Orbits
Re: Elliptical Orbits
Gday Louisa,
So, let's use what we know. There are virtually no nonconservative forces in planetary orbits, so mechanical energy is conserved, so
U + K = constant
so
-GMm/r + 1/2 mv^2 = constant
so small r (perihelion) gives more negative U gives higher K and thus higher v than large r. Which is also intuitive, of course: you fall downhill, you go faster.
See
http://www.animations.physics.unsw.edu. ... avity.html
for animations and more detail.
Joe
Your caution is well advised. That equation is, as you said, for circular orbits and not true for elliptical ones.I know it sounds silly asI'm trying to explain speeds for objects in elliptical orbits,
So, let's use what we know. There are virtually no nonconservative forces in planetary orbits, so mechanical energy is conserved, so
U + K = constant
so
-GMm/r + 1/2 mv^2 = constant
so small r (perihelion) gives more negative U gives higher K and thus higher v than large r. Which is also intuitive, of course: you fall downhill, you go faster.
See
http://www.animations.physics.unsw.edu. ... avity.html
for animations and more detail.
Joe