# Universal Law of Gravitation problem

• MiniOreo1998
In summary: Don't be too upset if you don't get it right first time - just work out what you did wrong and fix it.
MiniOreo1998

## Homework Statement

The Earth has a mass of 5.98 x 1024 kg and the moon has a mass of 7.35 x 1024 kg. The distance from the centre of the Moon to the centre of the Earth is 3.84 x 108 m. A rocket with a total mass of 1200 kg is 3.0 x 108 m from the centre of the Earth and directly in between the Earth and Moon.

Find the net gravitational force on the rocket from the Earth and Moon.

If anyone spots any mistakes (or clearer ways that I could have written things out) let me know!

Thanks in advance, coming to this site and reading through some of the threads has started to boost my confidence.

Fg = m1 m2 / r2

## The Attempt at a Solution

Fg = m1 m2 / r2

Earth & Rocket: Fg (6.67 x 10-11) (5.98 x 1024) (1200) / (3.0 x 108)2

Fgnetrocket = 5.318 N

Moon & Rocket: Fg (6.67 x 10-11) (1200) (7.35 x 1022) / (8.4 x 107)2

Fgnetrocket = -0.8337 N

FgnetRocket, Earth 5.318 N + FgnetRocket, Moon (0.8337 N) = 4.48

Fgnetrocket = 4.48 N

You seem to be doing fine - though I did not check your arithmetic.
I have some tweaks for you:

Fg = m1 m2 / r2
Since you want to use SI units, that should be ##F_g=GMm/r^2## ... since force is a vector, maybe: $$\vec F = -\frac{Gm_1m_2}{r_{12}^3}\vec r_{12}$$ where r12 is the vector pointing from m1 to m2. This would give the force on m2 due to m1.

Fgnetrocket = 4.48 N

Good including the units - lots of people forget.
Don't forget to specify the direction the force acts in the answer ... you have implied earlier that a positive force is in the direction of the Earth, but you should say that in the answer too.

Since the only forces being considered are gravitational, you don't need the g subscript.
In the 1st two cases you don't need the net" either - the gravitational force on the rocket due to the Earth would be ##\vec F_E##, due to the Moon would be ##F_M## and the total gravitational force (from these two) is ##F_{net}## or ##F_{tot}## ... that approach avoids having to write out huge long subscripts all the time.

Confidence booster: You can also figure out what distance the rocket needs to be from the Earth for the two forces to be equal and opposite.

You are going to have to figure out how to tell if you have the right answers - you are training to solve problems where nobody knows the right answer after all.

## 1. What is the Universal Law of Gravitation?

The Universal Law of Gravitation is a physical law that describes the force of gravity between two objects. 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 do you calculate the force of gravity between two objects?

The force of gravity between two objects can be calculated using the equation F = G * (m1 * m2) / r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

## 3. What is the significance of the gravitational constant?

The gravitational constant, denoted by G, is a fundamental constant in physics that determines the strength of the gravitational force between two objects. It is a key factor in calculating the force of gravity and is used in numerous equations in physics, astronomy, and engineering.

## 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 decreases. Conversely, if the distance between two objects decreases, the force of gravity increases.

## 5. Can the Universal Law of Gravitation be applied to objects on Earth?

Yes, the Universal Law of Gravitation can be applied to objects on Earth. It is the same law that explains the force of gravity between the Earth and objects on its surface, such as people, buildings, and vehicles. However, on Earth, the force of gravity is also affected by other factors such as the mass and density of the Earth's materials.

• Introductory Physics Homework Help
Replies
5
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
18
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
860
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
5K
• Introductory Physics Homework Help
Replies
6
Views
12K
• Introductory Physics Homework Help
Replies
23
Views
2K
• Introductory Physics Homework Help
Replies
16
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
3K