What is the energy difference when the Earth's distance from the sun changes?

[physicsss]

The Earth's distance from the sun varies from 1.469 X 10^8 km to 1.530 X 10^8 km during the year. Take the Sun to be at rest.

(a) Determine the difference in the potential energy.


(b) Determine the difference in the Earth's kinetic energy.


(c) Determine the difference in the total energy between these extreme
points.

 

[Galileo]

What IS the potential energy of the Earth as a function of the distance from the sun?
And what is the total energy?
If you know that, these question are very simple.

 

[Chi Meson]

When dealing with planetary GPE, you can't use the formula PE = mgh because g does not remain constant. However, a the law of universal gravity formula (F=Gmm/r^2) provides a way out.

You can find the GPG of theplanet by multiplying the gravitational force times the distance, in this case r, to get GPG = -Gmm/r (notice, not squared).

The negative is following the convention that when r is infinite, then GPE is zero, so when you are near a planetary body, you are in a "potential well," sort of like a hole in the ground.

So use the mass of the sun and mass of the planet as the two "m's" and the two distances as "r" to find the two GPEs. What is the difference between them?

After that, apply the principle of conservation of energy.

 

[physicsss]

What is the kinetic energy of the Earth? What sort of things do I need to solve it? And what does total energy mean? part a +part b for one radius minus part a +part b for another radius?

 

[Galileo]

You should know the expression for the kinetic energy of a particle. (Treat the Earth as a particle in this problem). It's 1/2mv^2.
The total energy is simply the potential energy + kinetic energy. As always.

 

[physicsss]

So it is potential energy at one radius=1/2*m*v^2, and potential energy at another radius=1/2*m*v^2. Then subtract the two?

Also,I have a question about the sign. If I subtract I way I get a positive sign and another I get a negative sign...which one is right?

 

[Galileo]

Oh dear.

The KINETIC energy of the Earth is K=1/2mv^2 where v is the speed of the earth.
The POTENTIAL energy of the earh is V=-Gmm/r where r is the distance of the Earth from the sun. (As Chi Meson said).
Conservation of energy states: K+V=E where E is a CONSTANT, called the total energy of the system.

Can you take it from here?

 

[Chi Meson]

The question asks for the DIFFERENCE in KE and total E. YOu do not need to find the actual KE of the earth, just the amount by which it fluctuates. Use the LAw of Conservation of Energy, to answer part c first!