What if Earth had 2 moons? How would this affect the space race?

[Pico1]

So let's assume, that Earth had a second moon around half the size of our moon. It orbits pretty far, just enough to have a stable orbit in Earth's SOI. How would this affect the space race, and could such a moon exist?

[kerbiloid]

It would be thrown away or down by the major Moon, as it's almost at the very outer limit of stable orbits.

The space race would keep concentrating on the bigger and closer, more significant Moon, where they were going to build a base.

The flight would take 2..3 times more time, so Apollo should have more supplies, and be heavier. so the discussion about funding the Nova rocker would be running for decades.

[sevenperforce]

It would have to be in resonance with the current moon (a la the Galilean moons of Jupiter) to stay in a stable orbit.

With that sort of resonance in play, it might become possible to use gravity assists to transfer back and forth between the moons and LEO without as much propellant consumption, which would open up additional trajectories and mission configurations. With a smaller second moon, we'd also have a lower barrier to landing and thus potentially an earlier initial landing. This would, however, lead to a two-part race to gain "first" status over both bodies, which might have extended the space race for longer and led to more accelerated development.

[magnemoe]

2 hours ago, sevenperforce said:

It would have to be in resonance with the current moon (a la the Galilean moons of Jupiter) to stay in a stable orbit.

With that sort of resonance in play, it might become possible to use gravity assists to transfer back and forth between the moons and LEO without as much propellant consumption, which would open up additional trajectories and mission configurations. With a smaller second moon, we'd also have a lower barrier to landing and thus potentially an earlier initial landing. This would, however, lead to a two-part race to gain "first" status over both bodies, which might have extended the space race for longer and led to more accelerated development.

Good point, longer stay in space but lower dV requirement to land like Minmus. 
An problem with an outer smaller moon is formation, I guess it could be captured but then I expect something even smaller but still and multiple km sized asteroid in L4 or 5 would be so cool 

[Kerbart]

17 hours ago, kerbiloid said:

The space race would keep concentrating on the bigger and closer, more significant Moon, where they were going to build a base.

Are you crazy? With life altering questions on the line like is it really made out of mint icecream, not to mention that while further away (and on in inclined orbit) it's a lot easier to land on/ascend from, I bet that they'd go for Moonmus first.

[NFUN]

The US and USSR would race to be the first to land on a moon, and unless in this reality the Soviets were just behind America and could go for a landing on the second as a consolation price, the lower would give up while the winner went on to visit the other Moon just to run up the score

[Kerbart]

1 hour ago, NFUN said:

The US and USSR would race to be the first to land on a moon, and unless in this reality the Soviets were just behind America and could go for a landing on the second as a consolation price, the lower would give up while the winner went on to visit the other Moon just to run up the score

With prestige at play the winner wouldn't just visit the other moon to run up the score — they'd visit the other moon first as well, to deny their enemy the consolation price.

[kerbiloid]

13 hours ago, sevenperforce said:

It would have to be in resonance with the current moon (a la the Galilean moons of Jupiter) to stay in a stable orbit.

The Moon orbit is unstoppably raising, and the Earth:Moon mass ratio is much less than the Jupiter one.
So, no stable orbits in the Earth moon system.

13 hours ago, sevenperforce said:

With a smaller second moon, we'd also have a lower barrier to landing and thus potentially an earlier initial landing.

And at the same time no possibility to build a stable base, so much less interest from any view but the bare flag planting.

13 hours ago, sevenperforce said:

This would, however, lead to a two-part race to gain "first" status over both bodies, which might have extended the space race for longer and led to more accelerated development.

The first, close, big Moon is significant from the military and then-looking-actual industrial pov.

The second, far, small Moon would interest nobody but nerds.
While irl the lunar program was funded with active support of the military, the mini-moon would be waiting for its turn like the asteroids. 
I remember the decade-old posts there about the (ULAlian, not nuke) Orion flights to the asteroid, then to the near-Earth asteroid, then to at least a captured piece of stone in HEO.
These posts would stay actual in that reality, too, just the Orion's target name would change.
The same users, who are blaming SLS, would be doing it to Nova, that's all change.

In the USSR the space race was actively doubted by the military, who were not once asking for proper reinvestment.
The Korolyov's participation to the lunar program was forced, distracting him from his dream of life, the expedition to the Mars.

Originally, in 1920s-early 1930s, Korolyov and Glushko were just two of several tens of groups, developing rockets of more-or-less same level, never exceeding several hundreds of kgf thrust (~Aggregat-1&2).
They were arrested due to the struggle between the teams in the institute, and the opponents in the known collective denunciation were pointing at the fact, that the only results of their eight-year activities were a 200-kg winged missile with 30-kg payload, and a small glider with a small rocket drive, so the funds had been spent on nothing.
It was also playing a role, that (unlike for other development teams) their patron was marshal Tukhachevskiy, a big fun of then-hi-tech in army, so they were funded and raised as his protegee.
At the same time, this means that they were in low orbit at then-scandalous scam of the "dynamo-reactive guns of Kurchevskiy", when Tukhachevskiy was actively promoting recoilless guns and cannons everywhere, including tanks and heavy artillery, as a cheap replacemenr for the normal cannons.
Of course, this strange idea failed, after having eaten a lot of budget money and delaying the upgrade of artillery.
So, when the scam was stopped, all Tukhachevskiy's protegee were hit by recoil. Especially the most known ones. Especially spending  money without results. Especially conflicting with the solid-fuel department, who were providing actual results. (Though, the solid-fuel tops were executed a little earlier, due to the struggle between the teams and the parties.)

In 1940s Glushko had developed a 1.5-tf rocket engine for a glider, which became 1.1-tf after making it human-rated by another engineer.
I.e. corresponding to Aggregat 3&5, when Walter Thiel's Aggregat-4 engine was already 25..28 tf.

You should not think that on the German  side the things were going much wiser.
The whole  Aggregat series (which fruited into V-2) was starting from the idea of a long-range 14" artillery shell with a rocket engine, which would throw it farther than powder.
Originally the Aggregat-1 was to be stabilized by rotation, without gyroscopes or so, but on realizing that the rotation will prevent the fuel sucking, they decided to rotate the warhead, leaving the booster motionless.
After making the rotating warhead mockup and exploding the first and the only A-1 on start, they screwed the rotating warhead, and put the amateur "gyroscope" in the middle, launching the two and the only Aggregat-2 just once.
Realizing that the shell is failed, they began Aggregat-3 (<<< the in-war imprisoned Glushko is nearly here) shaped as a an aircraft bomb with an alcohol  booster inside. As they were trying A-3 and A-5 launches from He-111, we can presume that the idea of the shell turned into idea of rocket-propelled long-range bomb.
On failing the vertical launches of A-3, they turned to big rockets like A-4 (as big as a railroad carriage can contain, the fin span is 3.2 m), which were succesfully eating the German money on the sick (20% sorted out on the plant, 40% of launched had exploded), useless (1-2 human casualties per A-4) rocket program. That's because they hadn't imprisoned von Braun in time, lol.

Von Braun himself is a strange, murky persone, closely associated with another one, even murkier one, Hans Kammler, who was the head of secret weapon development and KZ camps development, but mistically lacks any attention.
The Aggregat series was developed not by von Braun alone, but by the whole department of arms, where von Braun was not the boss.
The key components like the engine (by Walter Thiel), the C&C, the aerodynamics were provided by other people.
Von Braun's role looks more like a curator, than like a real engineering developer.

His kinda developed A9/A10 project looks like a scam. While he was doing aerodynamic experiments with the models. the A10 engine was a pure fantasy, changed from six A-4 28-tf engines around the single nozzle to a 200-tf alcohol engine (the practicallyreached top limit of the alcohol engines is RD-103, 45-tf), so we can assume that beyond a couple of failed launches of winged A-4b, there was no serious development behind A9/A10.
The A11 and A12 stages for his space rocket "were using" the same never-developed super-engine, so they are just a pure scam, sold to Americans to prevent the von Braun's extradition to the British, who were glad to ask him about the London bombing.
All components of Saturn/Apollo were developed by the American companies, so the von Braun's role looks totally PR, and this in turn returns us from the romantic dreams to the real roots of the American lunar program, which are concentrated as Project Horizon.

Meanwhile in the far, snowed Russia.
After making the R-7, an ICBM useless as ICBM, Korolyov was putting all efforts on killing the hypergolic rocketry, which efforts had fruited into separation of the Yangel and Makeev rocket bureaus, and raising the Chelomei's bureau in ballistic missiles, and thus into dismissing the Korolyov's bureau from the military development and losing him leading position in space launches, he started developing N-1 (another cryogenic non-ICBM ICBM, without any possibility of further development) and the Martian ship.

The whole department in  bureau was developing the TMK (Heavy Martian Ship) under the Tikhonravov's leadership.
(Btw, Tikhonravov came into rocketry before Korolyov, he had developed the very first working semi-liquid engine in 1920s).
As ~5 t of canned supplies was looking too heavy for the crew of 3, they were developing a whole on-board space farm, with kitchengardens and animals.
A ten of agricultural plants would be farmed under the solar light, rabbits and some others would be herded to provide meat, chlorella vats would refresh ing the air, etc.
But as Mars is 1.5 times farther from Sun than the Earth, the sunlight is weak. So, they added a huge parabolic reflector to insolate the garden.
But on the Martian orbit the ship will be rotating every hour, so the garden would be shaded. So, they made the mega-mirror truss mechanically rotating.
But the motor needs energy. So, they added 15 t of fuel to rotate the mega-mirror truss.
Another part of command was developing 100-t Martian rovers with 6-m wheels, and other things.

Thus, the Korolyov's team was wisely spending the budget funds on the highly realistic designs, and competing with Yangel and Chelomei were doing all daily dirty work of ballistic and cruise missile development.
Meanwhile almost all rocket engines were being provided by the Kosberg and Isayev bureaus, but for some reason the heavy RD-253 was possessed by Glushko.

Khrushchev had formulated the lunar objective very clearly and simply: "We'll not give away the Moon to the Americans".
This can be treated as a PR flag planting, but all further development show that the most sober and insightful Soviet leader was meaning the practical aspect, to prevent the monopolization of the Moon by the opponent.

Thus, once Proton and E-8 crafts had provided the ability to destroy any American lunar base before it could become operational (see the underdeveloped Death Star destruction in SW), the lunar program was immediately stopped, and the Korolyov's fantasy space program as well.

So, the "Space Race" was existing only in the heads of PR journalists, and another moon would not affect it.

Edited January 30 by kerbiloid