Universal Gravitation and/or Tidal Forces?

In summary, the single moon of an Earth-like planet is causing tides that are slowing the planet's rotation at a rate of 7.00 x 10-7 radians/sec/century. The planet's mass is 6 x 1024 kg and its diameter is 12,600 km, while the moon's mass is 7.35 x 1022 kg and its orbit radius is 386,000 km. To determine the rate at which the moon's distance from the center of the planet is increasing, the universal gravitation equation and possibly tidal force equations can be used. This problem can be solved by showing the work on an attached sheet.
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Homework Statement


The single moon of an Earth-like planet creates tides on the planet that are slowing the planet’s rotation. The planet’s rate of rotation is decreasing at a rate of 7.00 x 10-7 radians/sec/century. The mass of the planet is 6 x 1024 kg, and its diameter is 12,600 km. The radius of the circular orbit of the moon about the planet is 386,000 km. If the moon’s mass is 7.35 x 1022 kg, at what rate is the moon’s distance from the center of the planet increasing? [You may assume that the planet is a uniformly dense sphere.] You must show your work on an attached sheet.

∆r/∆t= __________________ km/year

Homework Equations



I know we will need the universal gravitation equation. possibly, tidal force equations. Can anyone attempt this?

The Attempt at a Solution

 
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I am not sure where to start. I know we will need to use the universal gravitation equation, but I am not sure how. Can anyone help?
 

1. What is universal gravitation and how does it work?

Universal gravitation is a physical law proposed by Sir Isaac Newton, which 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. This means that the greater the mass of an object, the stronger its gravitational pull will be, and the further apart two objects are, the weaker their gravitational attraction will be.

2. How does the force of gravity affect the motion of objects?

The force of gravity affects the motion of objects by causing them to accelerate towards each other. This acceleration is commonly known as gravitational acceleration and is dependent on the mass of the objects and the distance between them. The greater the mass of the objects, the greater the gravitational force between them, resulting in a stronger acceleration. Additionally, the closer the objects are to each other, the stronger the force of gravity, resulting in a larger acceleration.

3. What are tidal forces and how do they work?

Tidal forces are a result of the gravitational pull of the moon and the sun on Earth's oceans. The moon's gravitational pull is stronger on the side of the Earth closest to it, causing a bulge in the ocean at that location. At the same time, the gravitational pull on the opposite side of the Earth is weaker, resulting in a smaller bulge. This imbalance in gravitational forces causes the tides to rise and fall.

4. How do tidal forces affect the Earth and other celestial bodies?

Tidal forces not only affect the Earth's oceans but also impact the Earth's crust and interior. The constant pulling and stretching of the Earth's surface due to tidal forces can cause minor earthquakes and volcanic activity. On other celestial bodies, such as the moon, tidal forces can cause heating and geologic activity. Tidal forces can also cause changes in the rotational speed and orbit of celestial bodies over time.

5. Is the force of gravity the same throughout the universe?

No, the force of gravity is not the same throughout the universe. It varies depending on the mass and distance of objects. Additionally, the presence of other nearby objects can also affect the strength of gravity. Therefore, the force of gravity can differ in different regions of the universe and can even change over time as objects move and interact with each other.

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