Understand Newton's law of universal gravitation

In summary, the problem involves calculating the size of the gravitational force acting on the Earth due to the sun, given the masses of both objects and their distance apart. Using the equation F = G(mE)(mS)/r^2, the attempted solution involved plugging in the given values and resulted in a calculator error. The correct solution involves calculating the composite constant (GmE/r^2) and multiplying it by the mass of the object mO, which can be found by converting the radius of the Earth to meters and using the value of 9.81 m/s^2.
  • #1
aligass2004
236
0

Homework Statement


http://i241.photobucket.com/albums/ff4/alg5045/1012540B.jpg

Consider the Earth following its nearly circular orbit (dashed curve) about the sun. The Earth has mass 5.98 *10^24 kg and the sun has mass 1.99 *10^30 kg. They are separated, center to center, by r=93 million miles=150 million km. What is the size of the gravitational force acting on the Earth due to the sun?

Homework Equations



F = G(mE)(mS)/r^2

The Attempt at a Solution



Pretty much I just plugged and chugged to try to get the answer, which of course of was incorrect.

F = (6.67*10^-11)(5.98*10^24)(1.99*10^30)/ (1.5*10^11)^2 = 3.53*10^66
 
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  • #2
Hi aligass2004,

aligass2004 said:

Homework Statement


http://i241.photobucket.com/albums/ff4/alg5045/1012540B.jpg

Consider the Earth following its nearly circular orbit (dashed curve) about the sun. The Earth has mass 5.98 *10^24 kg and the sun has mass 1.99 *10^30 kg. They are separated, center to center, by r=93 million miles=150 million km. What is the size of the gravitational force acting on the Earth due to the sun?

Homework Equations



F = G(mE)(mS)/r^2

The Attempt at a Solution



Pretty much I just plugged and chugged to try to get the answer, which of course of was incorrect.

F = (6.67*10^-11)(5.98*10^24)(1.99*10^30)/ (1.5*10^11)^2 = 3.53*10^66

I think you have a calculator error here. If you multiply these numbers together, you don't get an exponent of 66.
 
  • #4
aligass2004 said:
That was the problem. Thank you!

http://i241.photobucket.com/albums/ff4/alg5045/1012540D.jpg

Now it asks for the value of the composite constant (GmE/r^2), to be multiplied by the mass of the object mO in the following equation?

http://i241.photobucket.com/albums/ff4/alg5045/render.gif

What is the statement of the problem?

I'm assuming re is not the radius of the earth, or you could just calculate that quantity from what you already have. Are the forces cancelling on that object, or is something else happening?
 
Last edited:
  • #5
r is the radius of the earth. I still just don't understand what it's asking for.
 
  • #6
If you can, please post the entire problem (all parts, even those that you may not have gotten too yet) exactly as its written, and maybe I or someone else can help you interpret it.

If all you need is the gravitational constant G times the mass of the Earth divided by the radius of the Earth squared, you can find those quantitites easily (they are usually inside the covers of the first-year physics textbooks).
 
  • #7
"Now it asks for the value of the composite constant (GmE/r^2), to be multiplied by the mass of the object mO in the following equation?"


The solution to the composite constant is simply 9.8 m/s^2.

Convert the radius of 6.38*10^3 km to meters... which is 6,380,000 m
(GmE/r^2)= (6.67*10^-11)(5.98*10^24)/(6,380,000)^2

Calculate this and you will get 9.81 m/s^2
 

What is Newton's law of universal gravitation?

Newton's law of universal gravitation is a physical law that states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Who discovered Newton's law of universal gravitation?

Sir Isaac Newton, an English mathematician and physicist, discovered and published his law of universal gravitation in his famous work "Philosophiæ Naturalis Principia Mathematica" in 1687.

How does Newton's law of universal gravitation relate to the motion of planets?

Newton's law of universal gravitation explains the motion of planets in our solar system. It states that the gravitational force between two bodies is dependent on their masses and the distance between them, causing planets to orbit around the sun in elliptical paths.

What is the difference between Newton's law of universal gravitation and Einstein's theory of general relativity?

While Newton's law of universal gravitation explains the force of gravity between two objects, Einstein's theory of general relativity describes gravity as the curvature of spacetime caused by the presence of mass and energy. It is a more comprehensive and accurate theory of gravity, applicable to both small and large scales.

How is Newton's law of universal gravitation used in everyday life?

Newton's law of universal gravitation is used in many everyday applications, such as predicting the motion of satellites, calculating the weight of objects, and understanding the tides. It is also essential in fields such as astronomy, engineering, and navigation.

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