Gravitational fields are closely related to the concept of time dilation, a key aspect of Einstein's theory of general relativity. Time dilation in a gravitational field, also known as gravitational time dilation, states that time runs slower in stronger gravitational fields. This effect occurs because gravity curves spacetime, and clocks closer to a massive object (where the gravitational field is stronger) will tick more slowly compared to those further away. This phenomenon has been experimentally verified, for instance, by comparing the time measured by clocks on Earth's surface to those in satellites in orbit. Gravitational time dilation has practical implications in satellite-based technologies like GPS, where time differences due to gravitational fields must be accounted for.

Gravitational lensing is a phenomenon in astronomy where the gravitational field of a massive object, like a galaxy or a black hole, bends the path of light coming from a more distant object. This effect is significant because it allows astronomers to observe and study objects that would otherwise be too faint or obscured. The massive object's gravitational field acts like a lens, magnifying and distorting the light from the distant object. Gravitational lensing has provided insights into the distribution of dark matter, the structure of galaxies, and the expansion of the universe. It is a crucial tool in modern astrophysics, demonstrating the practical applications of Einstein's theory of general relativity.

Gravitational fields significantly influence the trajectories of comets in the solar system. Comets, which usually follow highly elliptical orbits, are affected by the gravitational pull of the Sun and, to a lesser extent, other celestial bodies like planets. As a comet approaches the Sun, it accelerates due to the increasing strength of the Sun's gravitational field. This acceleration causes the comet to speed up and its trajectory to bend, forming a part of its elliptical orbit. When the comet moves away from the Sun, the gravitational influence decreases, slowing down the comet and elongating its orbit. The specific trajectory of each comet depends on its initial velocity and the gravitational influences it encounters, illustrating Kepler's laws of planetary motion.

The concept of using gravitational fields for energy generation or propulsion in space travel, often referred to as "gravity assist" or "slingshot effect," is a practical and energy-efficient method used in space missions. Spacecraft can use the gravitational field of planets to gain speed without using additional fuel. By carefully planning a trajectory that brings a spacecraft close to a planet, it can be accelerated by the planet's gravity, gaining kinetic energy and altering its path. This technique has been successfully employed in several missions, like the Voyager and Cassini probes, allowing them to travel further and faster. However, it's important to note that while gravitational fields can be used for propulsion, they do not generate energy in the conventional sense but rather transfer kinetic energy to the spacecraft.

Variations in Earth's gravitational field play a crucial role in geophysical surveys and exploration. These variations can be indicative of different densities and structures beneath the Earth's surface. For example, denser materials such as rocks or minerals have a stronger gravitational pull, causing slight increases in local gravitational field strength. By measuring these variations, scientists can infer the presence and distribution of various geological features like mineral deposits, oil reservoirs, or underground cavities. Gravitational field mapping is an essential tool in resource exploration, environmental studies, and understanding Earth's geology. It allows for non-invasive exploration of the subsurface, providing valuable data for making informed decisions in resource management and environmental protection.