# Difference in energy not the same in different reference frames

• etotheipi
In summary, the conversation discusses the concept of kinetic energy and its relationship to different frames of reference. The participants also touch upon the idea of energy conservation and how it applies to rockets. It is clarified that although the change in kinetic energy may vary in different frames, the total energy remains conserved. The importance of considering the kinetic energy of the exhaust in calculations regarding rocket propulsion is also emphasized.
etotheipi
These quantities are evidently not equal unless v1 = v2, but surely the change in kinetic energy should be the same in different frames of reference? I was wondering what mistake or misconception I have made because this has been bugging me for a little while.

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VVS2000
etotheipi said:
surely the change in kinetic energy should be the same in different frames of reference? I was wondering what mistake or misconception I have made
Your analysis is correct. You have not made a mistake. The change in kinetic energy is indeed different in different reference frames.

You may be concerned about conservation of energy. Conservation is a separate issue. KE is frame variant, but energy is still conserved

rayoub
Dale said:
Your analysis is correct. You have not made a mistake. The change in kinetic energy is indeed different in different reference frames.

You may be concerned about conservation of energy. Conservation is a separate issue. KE is frame variant, but energy is still conserved

Thank you for your kind response, that makes a lot of sense.

The problem I was doing at the time concerned the minimum velocities and consequently energies required to get a satellite from the equator, moving at a linear speed of 0.5 km s-1, into a stable circular orbit of theoretical height 0 metres with a linear velocity of 7.9 km s-1, all relative to a stationary observer in space.

Suppose some amount of work E is done on the satellite by forces from the exhaust gases over some distance during "lift off" to increase its kinetic energy from that corresponding to 0.5kms-1 to that corresponding to 7.9 kms-1.

Switching to the perspective of someone moving with the satellite around the equator before "lift off", the exhaust gases also do some work on the satellite to increase its kinetic energy from 0 initially to that corresponding to 7.4kms-1 (the relative velocity from the moving observer).

The situations are identical, so it appears that the amount of work done by the rockets should also be the same. However, like you mentioned earlier, the differences in kinetic energy are different in different reference frames, so the amount of work we calculate as necessary to get the satellite to this speed are apparently different.

I have the feeling that the amounts of work needed to get the rocket to the required velocity are also different depending on the reference frame, but cannot find a concrete source of this. Furthermore, what value of energy would we quote if trying to figure out e.g. how much fuel to use?

Thank you so much for your help!

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etotheipi said:
The situations are identical, so it appears that the amount of work done by the rockets should also be the same.
Consider the work done by the rocket on the exhaust stream.

Dale
I too actually posted a similar question regarding friction and energy loss. Yeah even I don't know how changing your frame of referece will affect the energy dissipation

VVS2000 said:
I too actually posted a similar question regarding friction and energy loss. Yeah even I don't know how changing your frame of referece will affect the energy dissipation
If you count all the participating bodies, energy dissipation does not depend on the choice of reference frame. It is an invariant. It is only if one restricts attention to a single object (e.g. the rocket) that a net effect is seen.

This derives from Newton's third law. The same force pairs are there in both frames. The same points of application are there in both frames. The change of frame changes the relevant velocities of the participating objects equally. It follows that the works done by the two members of the force pair are changed equally and oppositely.

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etotheipi said:
Furthermore, what value of energy would we quote if trying to figure out e.g. how much fuel to use?
As @jbriggs444 alluded to in post 4, the key is to consider the KE of the exhaust. I would go so far as to say that all confusions about energy conservation in rockets is due to a failure to consider the energy of the exhaust.

If you work it out, it turns out that for a non-relativistic rocket the energy in the fuel is frame invariant and any differences in the rocket KE from frame to frame are entirely compensated by differences in the exhaust KE.

## 1. What is the concept of "difference in energy not the same in different reference frames"?

The concept of "difference in energy not the same in different reference frames" refers to the idea that the amount of energy observed in a system can vary depending on the reference frame from which it is measured. This is due to the fact that energy is a relative quantity and can be affected by factors such as motion and gravitational forces.

## 2. Why is it important to consider different reference frames when studying energy?

Considering different reference frames is important because it allows us to accurately measure and understand the energy of a system. Energy is not an absolute quantity and can appear differently depending on the observer's frame of reference. By taking into account different reference frames, we can avoid making incorrect assumptions about the energy of a system.

## 3. How does the theory of relativity relate to the concept of "difference in energy not the same in different reference frames"?

The theory of relativity, specifically the special theory of relativity, explains the relationship between energy and reference frames. It states that energy and mass are equivalent and that the observed energy of a system can vary depending on the observer's frame of reference. This is known as the principle of relativity and is a key concept in understanding the differences in energy in different reference frames.

## 4. Can you give an example of how "difference in energy not the same in different reference frames" can be observed?

One example is the Doppler effect, which is the change in frequency or wavelength of a wave as observed by an observer in a different frame of reference. This can be seen in the difference in pitch of a siren as a vehicle approaches and passes by an observer. The energy of the sound waves appears different to the observer depending on their frame of reference.

## 5. How does accounting for different reference frames impact our understanding of energy conservation?

Accounting for different reference frames is crucial in maintaining the principle of energy conservation. In a closed system, the total energy remains constant, but it may appear differently to different observers depending on their frame of reference. By considering all reference frames, we can accurately track and account for the energy in a system and ensure that it is conserved.

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