How Does Gravitational Potential Influence Kinetic Energy in Satellite Launches?

[koujidaisuki76]

There is a graph saying that at r=1.0 is the center of the moon..

A satellite of mass 1500 kg is launched from the surface of the planet. Determine the minimum kinetic energy at launch the satellite must have so that it can reach the surface of the moon.

The surface of the moon is r= 0.96.
mass of the planet is 2398800599 kg


To find minimum kinetic energy would you use:

-GMm/r or GMm/2r ?

And wouldn't finding the potential energy equal the kinetic energy?
why or why not caus ei get two different answers

 

[Nate810]

To find the minimum kinetic energy, you would use GMm/2r. This is because the formula for kinetic energy (KE) is 1/2 mv^2, and the formula for gravitational potential energy (PE) is GMm/r. To calculate the minimum KE required to reach the moon's surface, you would subtract the PE at the planet's surface (GMm/r) from the PE at the moon's surface (GMm/2r). This is because the KE must be equal to the difference in PE between the two locations. Therefore, the minimum kinetic energy required to reach the moon's surface is GMm/2r - GMm/r = GMm/2r. It is true that the KE must equal the difference in PE between the two locations. However, the KE and PE are not necessarily equal to each other as they represent different forms of energy. The KE represents the energy of motion, whereas the PE represents the energy stored in an object due to its position relative to other objects.

 

[m2003]

I would like to clarify and provide some information regarding gravitational potential and its relationship to kinetic energy and the given scenario.

Firstly, gravitational potential is a measure of the potential energy that a mass possesses due to its position in a gravitational field. It is typically represented by the symbol V and is measured in units of energy per unit mass (such as joules per kilogram). In this context, the graph mentioned in the content is likely showing the gravitational potential of the moon as a function of distance from its center.

In the given scenario, we are asked to determine the minimum kinetic energy required for a satellite to reach the surface of the moon from the surface of the planet. This can be calculated using the conservation of energy principle, which states that the total energy (kinetic + potential) of a system remains constant.

In this case, the initial kinetic energy of the satellite at launch must be equal to the sum of its potential energy at the surface of the planet and its kinetic energy at the surface of the moon. This can be represented mathematically as:

KE launch = PE planet + KE moon

Since the satellite is launched from the surface of the planet, its initial potential energy at launch is zero. Therefore, the minimum kinetic energy required at launch would be equal to the kinetic energy the satellite needs to reach the surface of the moon, which can be calculated using the formula:

KE moon = -GMm/r

Where G is the universal gravitational constant, M is the mass of the moon, m is the mass of the satellite, and r is the distance from the center of the moon (0.96 in this case).

To address the question about using GMm/r or GMm/2r, it is important to note that the formula for gravitational potential energy is given by:

PE = -GMm/r

Therefore, the potential energy at a distance of r from the center of the moon would be twice the potential energy at a distance of 2r from the center. This is because as the distance increases, the potential energy decreases and becomes more negative. Therefore, the minimum kinetic energy required would be the same regardless of whether we use GMm/r or GMm/2r.

In conclusion, finding the potential energy does not necessarily equal the kinetic energy in this scenario because the potential energy at launch is zero and the kinetic energy at the surface of the moon is not. However, the minimum kinetic energy required at launch would be equal to