At what height above Earth's surface is the energy required to lift a satellite to that height equal to the kinetic energy required for the satellite to be in orbit at that height ?(b) For greater heights, which is greater, the energy for lifting or the kinetic energy for orbiting ?

Explanation

To solve the problem, we need to find the height \( h_0 \) above the Earth's surface where the energy required to lift a satellite to that height equals the kinetic energy required for the satellite to be in orbit at that height.

### Step-by-Step Solution:

1. **Understanding Potential Energy Change**:
The change in gravitational potential energy (\( \Delta U \)) when lifting a satellite from the Earth's surface to a height \( h_0 \) is given by:
\[
\Delta U = U_f - U_i = -\frac{GMm}{R_e + h_0} + \frac{GMm}{R_e}
...