# Did space missions use Newton's Theory of Gravity

#### neerajsu

Did Apollo space missions use Newton's Theory of Gravity or Einstein's theory of general relativity?

What about current space missions?? Also, I heard from my friends that nowadays people no longer use Newton's theory of gravity for the current space missions. How true is this?

And which one of these is majorly in practical use. Einsteins general relativity or Newton's Theory of Gravity??

In my school I was taught only about Newtons Theory of Gravity and I'm definitely not very well versed in Einstein's general relativity.. but I would like to get some expert opinions on this.

Another question.
I was explaining to my friend about calculating earths mass. I came to a suggestion that earth mass could be calculated, but only with the knowledge of G, by say tossing a ball onto the ground and using Free fall acceleration(g) in newtons theory of gravity equation. But without the knowledge of G how did they come to know about earths mass? How did they compute value of G in the first place? Cause I don't see a practical/empirical way to compute Gravitational pull between two objects.

Thanks

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#### jambaugh

Science Advisor
Gold Member
It is not quite an "either or" proposition. In practical applications Einstein's theory will manifest as small corrections to Newtonian predictions. If these are smaller than the level of precision for the application then they can be neglected.

For getting to the moon and landing on it, Newton's theory is sufficient. The precision of e.g. thrust and rocket motor on/off timing is too low for the application of Einstein's corrections to matter. The Newtonian course is plotted, and aimed at and any errors are measured and remediated via correction thrusts. (Note such issues as venting gasses affect trajectory more than relativistic factors.)

Now the GPS system needs to take Einstein's theory into account since they must measure time to very high precision over a long span of time. (To get a GPS guided bomb to land within 1 meter of the target requires better than 3 nano-second precision in time keeping.)

#### D H

Staff Emeritus
Science Advisor
Did Apollo space missions use Newton's Theory of Gravity or Einstein's theory of general relativity?
They used Newtonian gravity.

What about current space missions?? Also, I heard from my friends that nowadays people no longer use Newton's theory of gravity for the current space missions. How true is this?
Except for missions to Mercury, there's no real reason to use general relativity. The errors resulting from using Newtonian gravity instead of general relativity are quite small. These errors build up over time, eventually becoming observable after a long period of time has passed. NASA does use general relativity to compute planetary ephemerides, but that's because the time spans are long. Space missions are short. For missions to the Moon such as the two satellites just sent into lunar orbit to better measure the Moon's gravity field, NASA still uses Newtonian mechanics.

Another question.
I was explaining to my friend about calculating earths mass. I came to a suggestion that earth mass could be calculated, but only with the knowledge of G, by say tossing a ball onto the ground and using Free fall acceleration(g) in newtons theory of gravity equation. But without the knowledge of G how did they come to know about earths mass? How did they compute value of G in the first place? Cause I don't see a practical/empirical way to compute Gravitational pull between two objects.

Thanks
The mass of the Earth cannot be assessed directly. What can be assessed directly is the product μe=G*Me. The standard gravitational parameter μe is very observable by looking at satellite orbits. This value is known to about 8 decimal places of accuracy. Compare that to G, which is known to only 4 places or so. G is one of the least well known of the fundamental constants. The Earth's mass is obtained by dividing μe by G. The uncertainty in the Earth's mass is almost entirely attributable to the uncertainty in G.

With regard to how G itself is assessed, that's typically done with a modernized variation of the Cavendish experiment.

#### pdyxs

Except for missions to Mercury, there's no real reason to use general relativity. The errors resulting from using Newtonian gravity instead of general relativity are quite small. These errors build up over time, eventually becoming observable after a long period of time has passed. NASA does use general relativity to compute planetary ephemerides, but that's because the time spans are long. Space missions are short. For missions to the Moon such as the two satellites just sent into lunar orbit to better measure the Moon's gravity field, NASA still uses Newtonian mechanics.
What does this mean for missions like Voyager? If NASA uses GR to compute planetary positions, then I'd assume that they'd use it for these longer missions, but you've also stated that they wouldn't use it unless they were going to Mercury... unless there's a difference between using GR to figure out where you're going and to figure out the gravitational pull on the spacecraft on the way...

#### sophiecentaur

Science Advisor
Gold Member
Did Apollo space missions use Newton's Theory of Gravity or Einstein's theory of general relativity?

What about current space missions?? Also, I heard from my friends that nowadays people no longer use Newton's theory of gravity for the current space missions. How true is this?

And which one of these is majorly in practical use. Einsteins general relativity or Newton's Theory of Gravity??

In my school I was taught only about Newtons Theory of Gravity and I'm definitely not very well versed in Einstein's general relativity.. but I would like to get some expert opinions on this.

Another question.
I was explaining to my friend about calculating earths mass. I came to a suggestion that earth mass could be calculated, but only with the knowledge of G, by say tossing a ball onto the ground and using Free fall acceleration(g) in newtons theory of gravity equation. But without the knowledge of G how did they come to know about earths mass? How did they compute value of G in the first place? Cause I don't see a practical/empirical way to compute Gravitational pull between two objects.

Thanks
These are two really excellent questions, neerajsu.
It is so 'handy' to use Newton for calculations and then to make appropriate corrections later.

Your question about gravity really shows what a problem Scientists have. In many ways, Science has to 'pull itself up by its own bootstraps', building one measurement on a previous one. It's interesting to wonder what a civilisation near another, different star would do about measuring its environment. How many of their actual 'numbers' would turn out to be the same as ours. Obviously e and ∏ would be the same but what of the others - c, for instance?

#### neerajsu

Thank you for your answers guys. Cleared my doubts.

#### phyzguy

Science Advisor
As you said, once you know G, you can calculate the mass of the Earth by measuring the acceleration of an object at the Earth's surface. For this reason, the Cavendish experiment, which measured G for the first time, is sometimes referred to as "weighing the Earth".

http://en.wikipedia.org/wiki/Cavendish_experiment

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