Gravitational potential energy plays a crucial role in the concept of escape velocity, which is the minimum velocity needed for an object to break free from a celestial body's gravitational influence. To escape the gravitational field, an object's kinetic energy must be equal to or greater than the gravitational potential energy it would have at an infinite distance (where GPE is zero). The escape velocity is calculated using the energy conservation principle, setting the kinetic energy (1/2 mv²) equal to the gravitational potential energy required to reach an infinite distance. This calculation is fundamental in space travel and astrophysics.

Yes, gravitational potential energy can be used to calculate the maximum height an object can reach when thrown upwards. When an object is projected upwards, its kinetic energy is gradually converted into gravitational potential energy. At the maximum height, all of the initial kinetic energy has been converted to GPE. By equating the initial kinetic energy (KE = 1/2 mv², where v is the initial velocity) to the GPE at the maximum height (GPE = mgh), one can solve for the maximum height h. This calculation is a practical application of the conservation of energy principle.

Gravitational potential energy is central to understanding tides and tidal energy. Tides are caused by the gravitational pull of the Moon and the Sun on Earth's oceans. The variation in gravitational pull at different points on Earth's surface creates a difference in gravitational potential energy, leading to the movement of water known as tides. In tidal energy systems, this movement of water, influenced by changes in GPE, is harnessed to generate electricity. Tidal energy plants convert the kinetic energy of moving water (influenced by changes in GPE due to tides) into electrical energy, making GPE a key concept in this renewable energy source.

The 'zero level' or 'reference level' for calculating gravitational potential energy is an arbitrary point chosen for convenience and can vary depending on the context. For instance, in building construction, it might be ground level, while for a satellite, it could be the Earth's surface or another reference point in space. This level can change based on the problem's requirements. What is important is the relative height (h) from this reference point. GPE is always relative to this chosen zero level, and changing the reference point will change the calculated GPE value.

At extreme heights, such as those reached by high-altitude balloons, the assumption of a constant gravitational field strength (g) becomes less accurate. As the distance from the Earth's surface increases, g decreases slightly. Therefore, for precise calculations at these altitudes, the variation of g with altitude must be considered. This involves using the formula g = G * (M / r²), where G is the gravitational constant, M is the Earth's mass, and r is the distance from the Earth's centre. The calculated g value is then used in the GPE formula, GPE = mgh, for more accurate results at extreme heights.