The Gravitational Force Between Two Asteroids Is $6.2 \times 10^8 \, \text{N}$. Asteroid Y Has Three Times The Mass Of Asteroid Z.If The Distance Between The Asteroids Is 2100 Kilometers, What Is The Mass Of Asteroid Y?A. $3.7 \times

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Introduction

The gravitational force between two objects is a fundamental concept in physics that describes the attractive force between two masses. In this article, we will explore the gravitational force between two asteroids, Asteroid Y and Asteroid Z, and use this information to determine the mass of Asteroid Y.

The Gravitational Force Formula

The gravitational force between two objects can be calculated using the following formula:

F = G * (m1 * m2) / r^2

where:

  • F is the gravitational force between the two objects
  • G is the gravitational constant (6.674 * 10^-11 N m^2 kg^-2)
  • m1 and m2 are the masses of the two objects
  • r is the distance between the centers of the two objects

Given Information

We are given the following information:

  • The gravitational force between the two asteroids is 6.2 * 10^8 N
  • Asteroid Y has three times the mass of Asteroid Z
  • The distance between the asteroids is 2100 kilometers

Converting Distance to Meters

Before we can use the gravitational force formula, we need to convert the distance between the asteroids from kilometers to meters. There are 1000 meters in 1 kilometer, so:

r = 2100 km * 1000 m/km = 2,100,000 m

Using the Gravitational Force Formula

Now that we have the distance in meters, we can use the gravitational force formula to determine the mass of Asteroid Y. We are given that the gravitational force between the two asteroids is 6.2 * 10^8 N, so:

F = 6.2 * 10^8 N

We are also given that Asteroid Y has three times the mass of Asteroid Z, so:

m1 = 3 * m2

where m1 is the mass of Asteroid Y and m2 is the mass of Asteroid Z.

Substituting these values into the gravitational force formula, we get:

6.2 * 10^8 N = G * (3 * m2 * m2) / (2,100,000 m)^2

Simplifying the Equation

Now we can simplify the equation by combining like terms:

6.2 * 10^8 N = G * (3 * m2^2) / (4,410,000,000,000 m^2)

Solving for Mass

To solve for the mass of Asteroid Y, we need to isolate m2 on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the coefficient of m2^2:

m2^2 = (6.2 * 10^8 N * 4,410,000,000,000 m^2) / (3 * G)

Now we can take the square root of both sides of the equation to solve for m2:

m2 = sqrt((6.2 * 10^8 N * 4,410,000,000,000 m^2) / (3 * G))

Calculating the Mass of Asteroid Y

Now that we have the mass of Asteroid Z, we can calculate the mass of Asteroid Y by multiplying the mass of Asteroid Z by 3:

m1 = 3 * m2

Substituting the value of m2 into this equation, we get:

m1 = 3 * sqrt((6.2 * 10^8 N * 4,410,000,000,000 m^2) / (3 * G))

Evaluating the Expression

Now we can evaluate the expression to find the mass of Asteroid Y:

m1 = 3 * sqrt((6.2 * 10^8 N * 4,410,000,000,000 m^2) / (3 * 6.674 * 10^-11 N m^2 kg^-2))

m1 = 3 * sqrt((2.734 * 10^22 kg^2 m^2 s^-2) / (1.998 * 10^-10 kg^-2))

m1 = 3 * sqrt(1.371 * 10^32 kg^2)

m1 = 3 * 1.17 * 10^16 kg

m1 = 3.51 * 10^16 kg

Conclusion

In this article, we used the gravitational force formula to determine the mass of Asteroid Y. We were given the gravitational force between the two asteroids, the distance between the asteroids, and the fact that Asteroid Y has three times the mass of Asteroid Z. By substituting these values into the gravitational force formula and solving for the mass of Asteroid Y, we found that the mass of Asteroid Y is approximately 3.51 * 10^16 kg.

References

Q: What is the gravitational force between two objects?

A: The gravitational force between two objects is a fundamental concept in physics that describes the attractive force between two masses. It is calculated using the formula F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.

Q: What is the gravitational constant?

A: The gravitational constant, denoted by G, is a fundamental constant of nature that describes the strength of the gravitational force between two objects. It is approximately equal to 6.674 * 10^-11 N m^2 kg^-2.

Q: How do I convert distance from kilometers to meters?

A: To convert distance from kilometers to meters, you can multiply the distance in kilometers by 1000. For example, 2100 kilometers is equal to 2,100,000 meters.

Q: What is the mass of Asteroid Y?

A: In the previous article, we calculated the mass of Asteroid Y to be approximately 3.51 * 10^16 kg.

Q: How do I calculate the mass of an object using the gravitational force formula?

A: To calculate the mass of an object using the gravitational force formula, you need to know the gravitational force between the object and another object, the distance between the objects, and the mass of the other object. You can then use the formula F = G * (m1 * m2) / r^2 to solve for the mass of the object.

Q: What is the significance of the gravitational force between two asteroids?

A: The gravitational force between two asteroids is an important concept in astrophysics and planetary science. It helps us understand the dynamics of asteroid systems and the formation of planetary bodies.

Q: Can you provide more examples of how to use the gravitational force formula?

A: Yes, here are a few more examples:

  • If the gravitational force between two objects is 10^9 N and the distance between them is 1000 m, what is the mass of the smaller object if the larger object has a mass of 10^5 kg?
  • If the gravitational force between two objects is 5 * 10^8 N and the distance between them is 5000 m, what is the mass of the smaller object if the larger object has a mass of 2 * 10^6 kg?
  • If the gravitational force between two objects is 2 * 10^7 N and the distance between them is 2000 m, what is the mass of the smaller object if the larger object has a mass of 5 * 10^4 kg?

Q: How do I use the gravitational force formula to solve problems involving multiple objects?

A: To use the gravitational force formula to solve problems involving multiple objects, you need to consider the gravitational force between each pair of objects and add them up. For example, if you have three objects A, B, and C, and you want to calculate the gravitational force between A and B, you need to consider the gravitational force between A and B, as well as the gravitational force between A and C and the gravitational force between B and C.

Q: What are some real-world applications of the gravitational force formula?

A: The gravitational force formula has many real-world applications, including:

  • Calculating the orbits of planets and moons
  • Determining the stability of asteroid systems
  • Understanding the dynamics of binary star systems
  • Calculating the gravitational force between objects on Earth, such as between a person and the Earth

Q: Can you provide more information on the gravitational constant?

A: Yes, the gravitational constant is a fundamental constant of nature that describes the strength of the gravitational force between two objects. It is approximately equal to 6.674 * 10^-11 N m^2 kg^-2. The gravitational constant is a dimensionless quantity that is used to calculate the gravitational force between two objects.

Q: How do I calculate the gravitational force between two objects using the gravitational constant?

A: To calculate the gravitational force between two objects using the gravitational constant, you need to know the masses of the two objects and the distance between them. You can then use the formula F = G * (m1 * m2) / r^2 to calculate the gravitational force between the two objects.