Counterintuitive Science: Orbital Mechanics

Imagine you're in a vehicle, say a car.

You see another car just ahead, cruising at a leisurely pace.

Hey it's your friend Bob!

Hi Bob!

So you step on the gas to approach his car.

To your horror, the harder you step on it, the further he drifts away.

But Bob is not changing his speed at all.

Eventually you start running out of fuel, but his car continues to recede in the distance.

How can this be!?!! What a nightmare!
















On 3rd June 1965, two American astronauts faced this exact scenario.

James McDivitt and Edward White of the Gemini 4 space mission had just reached low Earth orbit at the height of about 200km.

They were instructed by mission control to attempt an orbital rendezvous with its spent second stage (a part of the rocket), which was circling the Earth at a slightly higher orbit.

This task was important to learn how to dock vehicles together in space, so that space stations and lunar missions can become reality.

Accustomed to the normal rules of flight, McDivitt aimed his spacecraft directly at the spent stage and fired his rear thrusters to catch up with it.

To his surprise, and the surprise of engineers on the ground as well, the target drifted further and further away.

It appeared as if he had accidentally thrown his own spacecraft into reverse. But there was nothing wrong with his vehicle - it was speeding up in the forward direction.

What happened? This article explains it:

This was where Newtonian mechanics kicked in.

By increasing his craft’s speed, he had increased its distance from the earth. In this new, higher orbit, the craft’s linear velocity, measured in miles per hour, was greater than before.

But its angular velocity—the rate at which it was traveling around the earth, measured in revolutions per hour—was lower. As Kepler had pointed out, objects in low orbits will complete an orbit around the earth faster than those in high orbits, even though their linear velocity is lower.

Click here to read more about the mathematics behind Kepler's equation.

At low Earth orbit, small differences in orbital height result in large differences in angular velocity. Johannes Kepler calculated this more than 300 years ago, but I guess NASA's Gemini 4 team was not prepared for such a striking effect during actual spaceflight.

Orbital mechanics is counterintuitive - unlike what you see in movies like Star Wars, you can't always approach a target simply by flying straight toward it.

Now, back to the story.

Eventually, despite many attempts, the Gemini 4 vehicle did not get any closer to the target.

McDivitt used up so much propellant that his thruster tanks drained to half-full (or half-empty?) and they decided to give up to avoid jeopardizing other mission objectives. Mission control agreed.

Although it seemed like a failure, this entire exercise was very important for the spaceflight endeavour because:

NASA engineers and astronauts extracted a valuable lesson from this mission: It was difficult, if not impossible, to steer a spacecraft merely by eye. The orbital dynamics are so counterintuitive that—combined with the lack of references for judging distances—no human could do the job without help from electronic sensors.

Another space mission would be needed to practice this manoeuvre.

Success finally came at end of the year. On 15th December 1965, Gemini 6A came within 30cm of its target, a passive Gemini 7 spacecraft.

These are the spacecraft shown in the photo above (Gemini 7 as seen from Gemini 6A).

How did they achieve this?

Firstly, instead of aiming straight for its target, the Gemini 6A spacecraft approached from a lower orbit so that it can catch with Gemini 7.

Next, the crew of Gemini 6A now had an onboard computer in command of the last 400km of the approach. The vehicle gradually traded angular velocity for height in a series of thruster burns until the two vehicles were just 40m apart.

Finally, at this distance, the more familiar rules of flight do apply, and the astronauts could close the gap by manually firing the thrusters.

This is fairly routine now, but imagine what went through the minds of all the people involved on that June day in 1965:

Pressing forward makes you move backwards? WTF!!?!


Would you like to know more?
- Diet foods can make you fat