Understanding Newton's Law of Universal Gravitation

In summary, we can calculate the size of the gravitational force acting on the Earth due to the sun using the formula F=GMm/R^2, where G is the gravitational constant, M is the mass of the sun, m is the mass of the Earth, and R is the distance between them. Plugging in the given values, we get a force of 3.39x10^22 N.
  • #1
Ecterine
13
0
"Consider the Earth following its nearly circular orbit about the sun. The Earth has a mass mearth=5.98x10^24kg and the sun has mass msu=1.99x10^30kg. 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?

I'm still setting up the problem...

I think I use the equation Fg=G(m1m2 / r2).

r is the distance between the centers of the two objects.
G is the gravitational constant (so I just leave that as G, right?)

But, is the sun or the Earth m1?
 
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  • #2
Wait... I just realized how stupid of a question that is. Why do I do this when I'm so tired?
 
  • #3
K, so now for a better question!

Fg=G(5.98x10^24kg x 1.99x10^30kg / 150,000,000 km)
Fg=G(7.933 x 10^46)Am I on the right track? What do I do with the G?

I know that the gravitational constant G has a value G=6.67x10^-11 N x m2/kg2

If I plug the mass of the sun in as m2 it is...

G=6.67x10^-11 N x 1.99x10^30kg/kg2

but... now I'm lost. :(
 
  • #4
Fg=(6.67x10^-11 N x 1.99x10^30kg / kg2) (7.933 x 10^46)

:(
 
  • #5
Ecterine said:
"Consider the Earth following its nearly circular orbit about the sun. The Earth has a mass mearth=5.98x10^24kg and the sun has mass msu=1.99x10^30kg. 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?

I'm still setting up the problem...

I think I use the equation Fg=G(m1m2 / r2).

r is the distance between the centers of the two objects.
G is the gravitational constant (so I just leave that as G, right?)

But, is the sun or the Earth m1?


The formula for gravitation is F=GMm/R^2. Some people may prefer to rewrite it as F=GM1M2/R^2. Just need to take note that M1 or M is the primary mass and M2 or m is the secondary mass. In this question, the mass of Sun is taken to be M1 or M.

Data used:
Gravitational constant = 6.67x 10^-11 Nm^2kg^-2 = G
Mass of Sun = 1.99x 10^30 kg = M
Mass of Earth = 6.02x 10^24kg = m
Distance between Sun and Earth = 1.5x 10^11m = R

Force acting on Earth by Sun = GMm/R^2
= 3.39X 10^22 N
 
  • #6
Thank you! :)
 

1. What is Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravitation is a scientific law that explains the force of gravity between any two objects in the universe. It 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.

2. How did Newton come up with this law?

Newton developed this law when he observed the motion of objects on Earth and the movements of the planets around the sun. He combined his understanding of gravity with his laws of motion to come up with the theory of universal gravitation.

3. Does this law apply to objects of all sizes?

Yes, Newton's Law of Universal Gravitation applies to objects of all sizes, from tiny particles to large celestial bodies. The force of gravity may be very small for smaller objects, but it is still present and follows the same law.

4. How does the distance between two objects affect the force of gravity?

The force of gravity between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the force of gravity between them decreases. This is why we feel less gravity when we are farther away from the Earth's center.

5. Can this law be used to explain the motion of all objects in the universe?

Yes, this law can be used to explain the motion of all objects in the universe as long as they have mass. This law has been successfully used to predict the behavior of celestial bodies, such as planets, stars, and galaxies, and has been proven to be accurate through various experiments and observations.

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