Why Is the Binding Energy of a Satellite Equal to Its Total Energy?

[rpullo]

Homework Statement

If an orbiting satellite has a total energy of -1.4 x 10¹² J, then the binding energy is...

b. 1.4 x 10¹² J

Homework Equations

Eg = (-GMm)/r
Binding energy = (GMm)/2r

The Attempt at a Solution

I was just wondering why the answer is 1.4 x 10¹² J. Thanks

 

[ideasrule]

Isn't it because binding energy is the same thing as total energy, only positive?

 

[kerimek]

for any help!

The binding energy of a satellite is the amount of energy required to completely remove it from its orbit around a larger body, such as a planet or a star. In this case, the satellite has a total energy of -1.4 x 1012 J, which means that it has a negative energy. This indicates that the satellite is in a bound orbit, meaning that it is held in its orbit by the gravitational force of the larger body.

The binding energy can be calculated using the equation Binding energy = (GMm)/2r, where G is the gravitational constant, M is the mass of the larger body, m is the mass of the satellite, and r is the distance between them. Plugging in the given values, we get:

Binding energy = (GMm)/2r = (-6.67 x 10^-11 Nm^2/kg^2 * M * m)/(2 * r)

Since we do not have any information about the masses or distances involved, we cannot calculate the exact value of the binding energy. However, we can make a general statement that the binding energy will have the same magnitude as the total energy of the satellite, but with a positive sign. This means that the binding energy in this case would also be 1.4 x 1012 J.

In summary, the answer of 1.4 x 1012 J is correct because it represents the magnitude of the binding energy of the satellite, which is equal to the total energy in this case.