Question

How does the earth orbit the sun without losing energy ?

Answer 1

In terms of Newtonian theories, the answer is satisfactory but the reality can be understood by the overall energy of the universe and the energy of the earth individually. When we take the universe as a whole, the concept of constant energy is debatable but when it comes to the earth individually and by using the concept of gravitational radiation, the earth does lose some energy.

Complete answer:
It might sound strange that if the earth loses energy then it must follow a spiral orbit and crash with the sun. The doubt is true but it would take the earth $1\times {{10}^{13}}$ times more years than the current age of the universe. And our species of humans are on this planet for just $200000$ years and probably we will find an alternative by the time this happens.

Even if we limit the discussion to the kinetic energy, there is actually an increase in the kinetic energy due to solar tidal drag. And with the increase in kinetic energy, the earth loses twice the potential energy. This also explains the concept of gravitational radiation as when the earth gains kinetic energy, it gains orbital speed and spirals towards the sun due to the decrease in the potential energy.

Note: Due to the loss in the energy of the earth, the energy gets transferred into the solar tidal drag which ultimately results in the difference of the king and the neap tides.The Earth is always being pulled towards the Sun by gravity.