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I can't for the life of me understand why commander Jim McDivitt thought he could eyeball a rendezvous - point the nose and thrust . The futility of that technique is one of the first things even amateurs like me learn about orbital dynamics . They had plenty of trajectory experts - Bill Tindall and his team plus Buzz Aldrin was an expert on rendezvous.

The long comment chain below this answer highlights the mis-conception that NASA astronauts as a whole did not understand the orbital mechanics of docking.

As this comment points out, the mechanics was well understood at the time, and at least one astronaut had written a thesis on the topic a few years earlier:

... Aldrins thesis about orbital rendezvous - which turned out to be an important cornerstone for NASA - is from 1963, just two years prior. So I think its at least probably that not everyone was familiar with it. I think they were knowledgeable about orbital mechanics, but the quote is about rendezvous - which can be very counter-intuitive. Aldrins thesis is about exactly that factor ;) I think its more that they didn't have the proper procedures, not that they couldn't figure it out in theory. They would probably have absolutely loved a simulator like KSP just to learn procedures ;)

My emphasis added above.

See Line-of-sight guidance techniques for manned orbital rendezvous

• Author: Aldrin, Buzz


• Citable URI: http://hdl.handle.net/1721.1/12652
  


• Department: Massachusetts Institute of Technology. Dept. of Aeronautics and Astronautics


• Publisher: Massachusetts Institute of Technology


• Date Issued: 1963


• Description:


• Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1963.; Vita.; Includes bibliographical references (leaves 305-309).


• URI: http://dspace.mit.edu/handle/1721.1/12652


• http://hdl.handle.net/1721.1/12652


• Keywords: Aeronautics and Astronautics

Gemini 4 was the first unsuccessful try of a rendezvous. They sought at that times it should be possible to rendezvous from a short distance by simply thrusting towards the docking object. They had to learn it the hard way that this strategy works only on very, very short distances and in a short time.

The circumference of a low Earth circular orbit with a height of 200 km is 41,286 km. A distance of 100 m is only 2.4 parts per million of the full orbit. Hard to believe at that times that about 100 m is still too far away for "point the nose and thrust". How close is neccessary for a successful "point the nose and thrust" rendezvous would be another good question.

If we look at the orbit period of about 90 minutes, 1 minute seems to be too long for such a "point the nose and thrust" maneuver. But how short is short enough, some seconds?

An exact digital simulation of such a rendezvous maneuver may be done using a simple single personal computer these days but could not be done in real time using the largest available computers in 1965 lacking a sophisticated and fast graphic display.

But they were successful with Gemini 6A only a half year later.

For more information see this very similar question.

First, the Gemini IV maneuver was station-keeping, not rendezvous. Since the target was the just-separated upper stage, the two spacecraft were already rendezvoused, and point-and-burn would have worked if they'd done it properly.

According to the Gemini IV mission report, the main causes of station-keeping failure were a mix of procedural mistakes and inadequately-aggressive maneuvering:

Review of these figures shows that the velocity increments applied through 00:09:21 g.e.t. succeeded in reducing the separation rate, but left a residual rate of 1.5 ft/sec away from the launch vehicle. As a result, the range from spacecraft to launch vehicle increased to 0.84 nautical mile and the range rate increased to 6.5 ft/sec by 00:30:25 g.e.t. when corrective action was initiated...

At this point (00:52:00 g.e.t.) a relative velocity of 8 ft/sec normal to the line of sight existed. This velocity propagated into a separation distance of 1.6 nautical miles and a separation rate of 17 ft/sec by the time corrective action was initiated at 01:05:30 g.e.t. The corrective thrust applied was insufficient...

It appears that if a procedure had been followed that required the crew (1) to initially establish a clearly perceptible closing rate with the target at all times and (2) to again establish a perceptible closing rate any time the range became larger than several stage II lengths, then the closeup station-keeping goal could perhaps have been achieved.

During the station-keeping exercise, the critical nature of rate determination was demonstrated. After separation, following the four thrusts back toward the launch vehicle, a rate of 1.5 ft/sec away from the stage II existed, whereas, a rate toward it should have been established. The range was approximately 1800 feet at this time. Later, at the point of closest approach, an 8-ft/sec rate existed, normal to the line of sight, which should have been removed.

The ability of a flight crew member to determine rates of the target even in daylight is considerably impaired without a stable background or familiar objects in the foreground. At night, the ability to determine rates depends on the relative distance between two reference lights if they are both visible. If only one light is visible, the flight crew member's judgement depends on his ability to measure the intensity of the light, and, if this one light is flashing, the task becomes very difficult.

In short, by the time the crew established a trajectory towards the target, a considerable lateral velocity had built up, and they had no reference point to judge that velocity against. If they'd established a closing trajectory immediately after separation, they would have been able to use the upper stage as a reference; if they'd approached from a different direction, they would have been able to use the Earth or the background star field as a reference.

(And for you KSP players, the Gemini FDI doesn't come with target and anti-target markers.)