Calculating the Ratio of Moon and Earth Density | Gravitational Problem Solution

In summary, the mass of the Earth is 5.98*10^24 kg with a radius of 6370 km, while the moon has a mass of unknown value and a radius of 1738 km. The acceleration of gravity at the surface of the moon is 1.62 m/s^2. To find the ratio of their average densities, we can use Newton's law of gravity by finding the mass of the moon and comparing it to the mass of the Earth. At the surface of the Earth, a 1 kg mass would have a weight of 9.81 N, while on the moon it would have a weight of 1.62 N.
  • #1
nns91
301
1

Homework Statement



The mass of the Earth is 5.98*10^24 kg and its radius is 6370 km. The radius of the moon is 1738 km. The acceleration of gravity at the surface of the moon is 1.62 m/s^2. What is the ratio of the average density of the moon to that of the Earth ?


Homework Equations



New's law of gravity: F= G*m1*m2/r^2

The Attempt at a Solution



I understand that I need to find mass of the moon to get its density. How should I calculate the mass of the moon ??
 
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  • #2
Assume a 1 kg test mass and write a statement about what is true at the surface of the Earth and a similar statement for the same 1 kg mass at the surface of the moon.
 
  • #3
On the Earth it will have the weight of 9.81 N and on the moon its weight going to be 1.62 N. Is that what you are talking about ?
 
  • #4
Can I use Newton's Law of Gravity here ? But I don't know either F or r and one of the m though
 

1. What is the difference between mass and weight in relation to gravitational problems?

In the context of gravitational problems, mass refers to the amount of matter in an object, while weight refers to the force exerted on an object by gravity. Mass does not change, but weight can vary depending on the strength of the gravitational field.

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

The force of gravity causes objects to accelerate towards each other, which can affect their motion in various ways. For example, gravity can cause objects to orbit around each other or fall towards each other.

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

Newtons's law of gravitation states that the force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. Einstein's theory of general relativity provides a more comprehensive explanation of gravity, taking into account the curvature of space and time caused by massive objects.

4. How does the strength of gravity vary on different planets or celestial bodies?

The strength of gravity varies depending on the mass and radius of a planet or celestial body. Generally, larger and more massive objects have a stronger gravitational pull. For example, the force of gravity on Earth is stronger than on the Moon due to Earth's larger mass.

5. Can gravity be canceled out or eliminated?

No, gravity cannot be canceled out or eliminated. It is a fundamental force of nature that affects all objects with mass. However, the effects of gravity can be counteracted by other forces, such as the centrifugal force experienced by objects in orbit around a larger body.

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