# What is the mathematics that took us to the moon?

1. Jan 14, 2016

### AndrewRibeiro

Are Newton's three laws all that was needed for the science that got us to the moon? Or did we need Einstein's theories to get there? I just started studying physics last week, so forgive me for my baseness.

2. Jan 14, 2016

### axmls

We did not need Einstein's theories to get there. Taking relativistic effects into account would only correct us by a few centimeters or so. We, of course, also needed all of the extensions of Newton's laws, i.e. all of the mechanical engineering, aerodynamics, etc. that would allow the spaceship to be structurally sound, so you also need to bring the equations of material mechanics into things. Also, thermodynamics had to be involved. Fluid mechanics for the aerodynamics, almost a century of telecommunications technology. So I'd say you can't break it down to just Newton's laws. We stood on the shoulders of many more giants to go to the moon.

If you're talking only in terms of orbital mechanics, though, no, no relativity was used. Newton's equations are good enough (though I'm sure we utilized mathematical methods introduced long after Newton to solve those equations).

3. Jan 14, 2016

### rcgldr

A bit of trivia, part of Apollo's navigation involved something like a sextant and star charts, to accurately locate position and orientation of the Apollo, which was needed to make accurate thrust based transitions in and out of orbit from the earth and moon. Earth based systems could track the Apollo for the earth to lunar transition, but the moon to earth transition thrust occurred past the far side of the moon.

http://www.spaceartifactsarchive.com/2013/05/the-star-chart-of-apollo.html

4. Jan 14, 2016

### Staff: Mentor

Welcome to PF!
Four laws.

5. Jan 14, 2016

### AndrewRibeiro

Four?

6. Jan 14, 2016

### AndrewRibeiro

Is this like telling a freshman there's a pool on the roof?

7. Jan 15, 2016

### jbriggs444

What I think Russ is getting at is that Newton's "three" laws alone do not say much about gravity.

8. Jan 15, 2016

### Staff: Mentor

Yep. There was a slight disconnect in your OP, where you are clearly implying gravity by mentioning relativity, but gravity is a different law from the three laws of motion.

If I wanted to get super nitpicky, I'd probably say there were lots of others needed for the technology, including from Newton, like his law of cooling.

9. Jan 15, 2016

### SteamKing

Staff Emeritus
These navigation tools were used on Apollo because things we take for granted, like cheap calculators and small computers, weren't available or were too big to put in the spacecraft.

This article discusses the guidance system equipment which was used on most Apollo missions:

https://en.wikipedia.org/wiki/Apollo_Guidance_Computer

10. Jan 16, 2016

### rcgldr

If I recall correctly, the NOR gates uses in that computer were more resistant to the radiation experienced in space that other technolgies of that era.