Orbital Speed and Buzz Out Loud

One of my favorite podcasts to listen to while driving or mowing the lawn is [Buzz Out Loud](http://bol.cnet.com). Buzz Out Loud (BOL) is basically just a tech-based podcast, but very entertaining. Anyway, as part of my attention seeking disorder, I try to get mentioned on the show. I succeeded once when I posted my [Optimal Commuting Speed Calculator](http://www.dotphys.net/page1/page10/efficiency/calculator.html). When I heard Tom and Rafe talking about orbital speeds, I realized this was my chance. Find any tiny flaw in their reasoning and I could perhaps come up with a comment worthy of their show.

The BOLers were talking about the astronaut that dropped a tool bag in space. Rafe said: *"everything in orbit is moving at the same speed"*. The idea behind his statement is mostly correct - but not completely. Let me take this opportunity to talk about orbital motion (from a very basic standpoint). Oh - don't forget, I [talked about gravity and weightlessness in a previous post](http://scienceblogs.com/dotphysics/2008/09/gravity-weightlessness-and-a…)

There are two important concepts needed to look at orbital motion (well maybe three).


First is the gravitational force: (in scalar form)

![Ngrav 1](http://scienceblogs.com/dotphysics/wp-content/uploads/2008/11/ngrav-1.j…)

The direction of the gravitational force is such that it attracts the two objects.

**Circular Motion**

When an object moves in a circular motion (at a constant speed) it has an acceleration towards the center of the circle with a magnitude of:

![Centaccel 1](http://scienceblogs.com/dotphysics/wp-content/uploads/2008/11/centaccel…)

Here v is the magnitude of the velocity (the speed) and r is the distance from the object to the center of the circle. For orbital motion, r is the distance to the center of the Earth (if it is in a circular orbit).

**Orbital Speed**

So, how about something moving in an orbit. In this case, there is a force on the object (tool bag or space shuttle or astronaut). The force is the gravitational force. This force makes the object accelerate.

![Orbit 23](http://scienceblogs.com/dotphysics/wp-content/uploads/2008/11/orbit-23…)

This diagram violates my rule of combining force and non-force vectors. Oh well. If I just look at Newton's second law in the r-direction (which is towards the center of the orbit), then:

![Circsdf 2](http://scienceblogs.com/dotphysics/wp-content/uploads/2008/11/circsdf-2…)

Here I am using M for the mass of the Earth and m for mass of the orbiting object. I can now solve for v:

![Orbitalv 1](http://scienceblogs.com/dotphysics/wp-content/uploads/2008/11/orbitalv-…)

This is enough to get to my point:

**All objects DO NOT orbit at the same speed**

Since the orbital speed depends on r, the farther from the Earth, the slow the object goes.

From a certain point of view, Rafe was correct. The dropped tool bag WAS at the same orbital radius, so it would be going about the same speed as other objects in that area.

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Idiot ISS FUBAR should orbit in equilibrium configuration with its long axis normal to the geoid. NASA likes it to fly tangent. There is hardly any true free fall volume within ISS FUBAR as reaction wheels keep it pivoting and residual air resistance does its thing. Why wasn't everything loose tied with a tether? Loosing an asstronaught is no big deal - we've got lots eager to get radiation cataracts - but the equipment is expensive and space junk is deadly on impact.

Do all objects in geosynchronous orbit travel at nearly the same relative velocity? I'm thinking mabe Rafe had mis-applied the similar velocities of geosynchronous orbits with the space station which shich has a non-geosynchronous orbit.

shut up Al.

holy crap, i didnt know that such an amazing site exits. great job man, really really love this site.

From a certain point of view, Rafe was correct. The dropped tool bag WAS at the same orbital radius, so it would be going about the same speed as other objects in that area.