Gravitational Attractive Force Between Sun and Earth

[brockrwood]

My child, Naomi, was working on a homework problem in their Astronomy for non-science majors class in college. They texted me about it.

The problem involved the gravitational force between the Sun and Earth and between the Sun and Mars.

The problem, which I won’t go into here unless someone wants me to, got me to thinking. What IS the gravitational force between the Sun and the Earth? It can’t be that hard to calculate, right? It is some sort of application of the “inverse square law”, right?

So I looked up Newton’s gravitational attraction equation for the gravitational attraction between any two objects. It is an application of Newton’s second law of motion, Force = mass * acceleration.

The equation is F = G ((Mm)/r^2)

The equation is not hard to do with pencil and paper. The hardest part is remembering how to multiply and divide using scientific notation. The second hardest part is keeping the complicated units of each value straight.

Here it is.



So, anybody who knows middle school math can run this equation.

Thank you, Sir Isaac!

 

[darrenf]

Chat GPT comes up with 3.567×1019 Newtons.

 

[brockrwood]

For the record, the force that attracts the Earth to the Sun and the Sun to the Earth is about 3.5573333 x 10^22 Newtons. That’s a BIG force.

 

[brockrwood]

Chat GPT comes up with 3.567×1019 Newtons.

View attachment 629526

ChatGPT! Pshaw! I have my mechanical pencil and a calculator!

 

[darrenf]

ChatGPT! Pshaw! I have my mechanical pencil and a calculator!

View attachment 629527

Yeah, I used to have all that too when I was studying physics, but I use the tools at hand to save time. Plus it removes the possibility of my fat fingers messing something up on my TI calculator.

 

[brockrwood]

Byjus.com says I am right. I have no idea what byjus.com is but, since it is on the internet, it must be true. ;-)

https://byjus.com/question-answer/c...ge-distance-between-the-two-is-1-5-x-1011-m/#

 

[darrenf]

Byjus.com says I am right. I have no idea what byjus.com is but, since it is on the internet, it must be true. ;-)

https://byjus.com/question-answer/c...ge-distance-between-the-two-is-1-5-x-1011-m/#

Hmm, seems we found an issue with Chat GPT.
You seem correct.

 

[brockrwood]

Well, maybe both answers are right. I think I was calculating the force at the point in space where the force the Sun exerts on Earth (call it F1) is equal to the force the Earth exerts on the Sun (call it F2). That would be the point in space where you can find the overall force between the Sun and the Earth, no? See screenshot of diagram.

 

[darrenf]

And now CHAT GPT has checked out on me. LOL

 

[darrenf]

 

[brockrwood]

Chat GPT is still off by a power of 10.

It would be 35.53 x 10^21

To reduce that to a decimal under 10, you move the decimal one place to the left. Then you add 1 to the exponent on the 10. 3.553 x 10^22.

 

[darrenf]

Chat GPT is still off by a power of 10.

Chat GPT is still off by a power of 10.

It would be 35.53 x 10^21

To reduce that to a decimal under 10, you move the decimal one place to the left. Then you add 1 to the exponent on the 10. 3.553 x 10^22.

Yep. I'm done teaching our mechanical overlords for today.

 

[darrenf]

Meh, I went back to it. Not sure it will get it right after this, but who knows.

 

[kuririn]

Chat GPT comes up with 3.567×1019 Newtons.

A while back I asked Chat GPT about model rocket stability.
It gave me an incorrect definition of caliber of stability.
https://www.rocketryforum.com/threa...del-rocketry-tasks.178984/page-4#post-2416773
I would never use Chat GPT if I wanted a correct answer.

 

[darrenf]

A while back I asked Chat GPT about model rocket stability.
It gave me an incorrect definition of caliber of stability.
https://www.rocketryforum.com/threa...del-rocketry-tasks.178984/page-4#post-2416773
I would never use Chat GPT if wanted a correct answer.

I've had good results, especially using it to write powershell scripts. It's still in the way early stages though.

 

[darrenf]

I finally got it to recognize where it went wrong.

 

[cerving]

Big surprise... ChatGPT probably would not have been the tool to use to get to the Moon.

 

[Hobie1dog]

So, anybody who knows middle school math can run this equation.

wrong, not me

 

[jsdemar]

Now find the velocities required for Earth and Mars to stay in their orbits.

 

[KenECoyote]

(Before ChatGPT and fancy calculators!)

 

[brockrwood]

(Before ChatGPT and fancy calculators!)

I played with using logarithm tables to do multiplication and division of large numbers. You know, a la 1910.

Outcome: Yes, using logarithm tables will let you multiply and divide big, arbitrary mumbers. Especially for the long division, the logarithm tables speed things up. Accuracy is limited to about three decimal places.

Using a slide rule will let you multiply and divide large numbers but the accuracy is less. Also, I have yet to completely master how to use a slide rule.

So, when TI released the TI-30 pocket calculator in the 1970’s, which did away with logarithm tables and slide rules, it truly was a revolution in speeding up how fast calculations could be done. At least for students and the general public who could not afford expensive calculators and computers. Proletarian guys like me.

 

[Lotronex]

I tried it using Wolfram Alpha, much better response.

Steph-by-step unfortunately requires a pro account.

 

[brockrwood]

wrong, not me

Yes, you can, @Hobie1dog . I am a philosophy major. If I can do it, you can do it. I did have to brush up on how to multiply and divide with scientific notation.

Because the formula specifies the units for the entire equation and the result, I did not have to master how the units reduced to Newtons.

 

[Hobie1dog]

Thanks to Neil deGrasse Tyson how much more interested I'm interested in astronomy and astrophysics then I ever was, and this is at age 67.

 

[brockrwood]

Thanks to Neil deGrasse Tyson how much more interested I'm interested in astronomy and astrophysics then I ever was, and this is at age 67.

Lifelong learning, brother. It’s awesome and satisfying.

 

[bjphoenix]

A while back I asked Chat GPT about model rocket stability.
It gave me an incorrect definition of caliber of stability.
https://www.rocketryforum.com/threa...del-rocketry-tasks.178984/page-4#post-2416773
I would never use Chat GPT if I wanted a correct answer.

I've read a few things about chat gpt, it seems that the way it is trained it might have inaccurate information sometimes. It isn't intended to be an encyclopedia.

Using a slide rule will let you multiply and divide large numbers but the accuracy is less. Also, I have yet to completely master how to use a slide rule.

I'll bring one up there one of these days. The slide rule is limited to essentially 3 significant figures of accuracy, but it can handle any value of exponent you have. I learned how to keep track of the decimal in my head as I worked the slide rule, it is easier than you might think.

I seem to remember that the very first TI calculators did not do scientific notation, if you were trying to deal with very large or very small numbers you could overflow the thing. The first time I saw someone with an HP35 was in physics class. There are some calculations that have constants with large exponents, or small exponents I can't remember. I watched someone show a calculation to another person- he keyed in the number then the exponent, then the second number and exponent. When he hit multiply the calculator gave the answer and the correct new exponent.


Back to the OP- now that you have calculated the pull the earth has on the moon, check it by calculating the centrifugal force of the moon in its orbit and see if you get the same answer.

 

[brockrwood]

figures of accuracy, but it can handle any value of exponent you have. I learned how to keep track of the decimal in my head as I worked the slide rule, it is easier than you might think.

I have a slide rule I got secondhand. It’s a plastic, German one. From the late 60’s or early 70’s I think.

I played with it and got it to do simple multiplication and division for me.

I was always squinting to try to get as accurate an answer as possible. It did not seem like I was getting 3 significant digits of accuracy. Maybe it was an inexpensive student model?

In the wikipedia article about the TI-30 it says that a TI-30 at $24.95, in 1976, cost less than some high end slide rules. That speaks volumes. Slide rules must have died off quickly.

 

[Alan15578]

I played with using logarithm tables to do multiplication and division of large numbers. You know, a la 1910.

Outcome: Yes, using logarithm tables will let you multiply and divide big, arbitrary mumbers. Especially for the long division, the logarithm tables speed things up. Accuracy is limited to about three decimal places.

Using a slide rule will let you multiply and divide large numbers but the accuracy is less. Also, I have yet to completely master how to use a slide rule.

So, when TI released the TI-30 pocket calculator in the 1970’s, which did away with logarithm tables and slide rules, it truly was a revolution in speeding up how fast calculations could be done. At least for students and the general public who could not afford expensive calculators and computers. Proletarian guys like me.

In many physics problems, they are happy with an order of magnitude answer. Slide rule accuracy is more than adequate for most problems.

I started with slide rules and bought the TI-30 as soon as it became available. It cost about 100 1974 bucks, and it only had 5 operations. You still needed the log and trig tables to solve many problems. I did a lot of CP calculations, and the slide rule was significantly faster. It takes more time punch in digits and other keys.

 

[brockrwood]

I have a slide rule I got secondhand. It’s a plastic, German one. From the late 60’s or early 70’s I think.

I played with it and got it to do simple multiplication and division for me.

I was always squinting to try to get as accurate an answer as possible. It did not seem like I was getting 3 significant digits of accuracy. Maybe it was an inexpensive student model?

In the wikipedia article about the TI-30 it says that a TI-30 at $24.95, in 1976, cost less than some high end slide rules. That speaks volumes. Slide rules must have died off quickly.

It is Dietzgen slide rule. Something like this.

https://www.ebay.com/itm/1263115398...T40ghdhRTC&var=&widget_ver=artemis&media=COPY

 

[bjphoenix]

In many physics problems, they are happy with an order of magnitude answer. Slide rule accuracy is more than adequate for most problems.

I started with slide rules and bought the TI-30 as soon as it became available. It cost about 100 1974 bucks, and it only had 5 operations. You still needed the log and trig tables to solve many problems. I did a lot of CP calculations, and the slide rule was significantly faster. It takes more time punch in digits and other keys.

I remember the TI-30 being about $150 when it first came out and that was probably 1973. The lesser calculators such as the original TI model were closer to $100. TI-30 was the first relatively low priced calculator that included square roots. HP-35 had that and more but it was $400. I was in college and trying to determine how to afford a TI-30. According to consumer price index that $150 would be about $1,030 in 2023 dollars.

Slide rule accuracy is to 3 significant digits, and the last digit can be +/- 1 or 2. This is sufficient accuracy for engineering when you don't know the loads, the material sizes or the material properties even that accurately. It would not be good enough accuracy for financial applications such as calculating interest, taxes, etc.