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  • Subject area(s): Engineering
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  • Published on: 7th September 2019
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In 1916, Einstein wrote the general theory of relativity, which included his relativistic laws. These laws insisted that black holes exist (Thorne, 2014). Black holes were previously called “gravitationally completely collapsed star”, but in 1967, John Wheeler renamed this to its name today (Bouwhuis, 2009). Black holes are made of warped time and warped space (Thorne, 2014). The event horizon is believed to be the region where humans can no longer perceive the warped space, so it appears black to us. Even light can’t escape the event horizon due to the enormous amount of gravity. Inside of this warped space is a singularity, a point that is infinitely warped (Thorne, 2014). There is also a region of a Kerr black hole called the ergosphere or the ergoregion. This is an area outside of the event horizon where energy grows indefinitely if the angular momentum of a particle takes large negative values (Zaslavskii, 2013). This acceleration of particles is a universal property of the ergosphere. (Zaslavskii, 2013)

There are four different types of black holes: stellar-mass, supermassive, intermediate mass, and micro. Stellar mass black holes are remnants of stars and form directly from supernova explosions (Bouwhuis, 2009). Supermassive black holes are believed to lie in the centers of most galaxies and are most likely formed by the merger of smaller black holes (Bouwhuis, 2009). Intermediate mass black holes are extremely rare, produce intense bursts of gravitational waves, and are likely to be formed from the merging of smaller black holes (Bouwhuis, 2009). Micro black holes have a very low mass where quantum effects play a role; therefore, they are poorly understood and are predicted to have a very short lifetime (Bouwhuis, 2009). There are also two kinds of black holes. Schwarzchild black holes do not rotate (Campanelli, 1999) and are electrically neutral (Bouwhuis, 2009). Kerr black holes rotate and have poles (Bouwhuis, 2009) and have an accretion disk that is made up of matter (Zaslavskii, 2013).

Black holes can be formed by a neutrino-energy desposition (in a neutron star). A shock is produced as the inner core collapses and bounces. This shock stalls due to dissociation and neutrino losses and leaves behind an unstable entropy gradient. This gradient creates a convective layer at the edge of the stalled shock, and this layer goes down to the proto-neutron star surface. As the star begins to collapse, the convection layer builds pressure on the shock. If the shock pressure overcomes the convection layer pressure, the star will collapse and turn into a black hole. The convective layer could also push the shock outward, creating a supernova. As the supernova shock travels outward, it decelerates. If the shock and the material decelerates below the escape velocity, it will fall back into the neutron star and push the star above its mass limit, creating a black hole. (Fryer, 1999)

Main sequence stars can also turn into black holes. In this star, hydrogen fuses to helium, generating large amounts of heat and creating a temperature gradient. This temperature gradient produces a pressure gradient, which keeps the star from collapsing. When the hydrogen and helium runs out, gravity takes over and causes the star to collapse on itself. (Bouwhuis, 2009)

Space studies are important for the advancement of fundamental scientific views of the Earth, Solar System, and the Universe. These studies are hindered by the practical problem relating to the aspects of the development of science, engineering, and economics. Another problem is the large scaled experiments require planning to collect maximum data at a minimum cost. Spacecraft routes should also minimize the cost of the mission and maximize the scope of the studies. The concept of multipurpose space missions serves as a solution to this problem. These missions involve planning a trajectory where the craft passes by a series of celestial bodies to be explored. The gravity fields of these bodies can be used to change the trajectory of the craft; reducing the energy cost and expanding the scope of the research. (Labunsky, 1998)

A spacecraft that used the gravitational slingshot maneuver was the Pioneer 10. The purpose of the mission was to escape from the Solar System. The Pioneer 10 was originally in an elliptical orbit around the Sun. It encountered Jupiter and gravitational assist was used to increase its speed and make a hyperbolic escape orbit away from the Solar System. The desired result of this maneuver was created by estimating the necessary magnitude of a multistage combination of rockets to provide an increase in speed and kinetic energy, and a change in direction of the craft. This observed gain in kinetic energy was entirely dependent on the fact that the planet was in motion. To extract energy from a planet, the spacecraft must exert a force on the planet and do a negative amount of work on the planet. The force must act over a distance. The distance traveled is independent of the mass of the planet, and so the work done is significant. (Van Allen, 2003)

For a spacecraft to increase kinetic energy, the angle of the craft after passing the planet has to be less than the angle of the craft before passing the planet. The increase in the kinetic energy of the spacecraft is caused by the decrease in the kinetic energy of the planet. Due to the planet’s enormous inertial mass, this kinetic energy is decreased by a very small fraction. (Dykla, 2004)

In the ergosphere, a particle can break in two, with one piece falling into the black hole and the other being flung into infinity. This phenomenon is called the Penrose Process. The energy gain is caused by the negative energy of the ergosphere-trapped particle falling into the black hole. The negative energy particle must originate in the ergosphere, the only domain of space-time where this particle can exist. Using the rotational energy of a black hole is possible if negative energy and momentum is absorbed by the black hole. (Lasota, 2014)

Some magnetic field lines connect a Kerr black hole with the disk rotating around it, transferring energy and angular momentum between the two. If a black hole rotates faster than the disk, then energy and angular momentum is extracted from the black hole and is transferred to the disk, where it eventually radiates to infinity. If a black hole rotates slower than the disk, energy and angular momentum is transferred from the disk to the black hole, and the disk accretes onto the black hole. (Li, 2000)

Gargantua weighs approximately 100 million Sun’s. Its event horizon is 1 billion kilometers, which is the same as Earth’s orbit around the Sun. A typical accretion disk emits radiation so intense that any nearby human would be fried at 100 million degrees. Gargantua’s disk is anemic at about three thousand degrees, so it emits a lot of light but very little radiation. (Thorne, 2014)

After tidal forces move the Endurance away from Mann’s planet, the ship has a certain amount of angular momentum. This is the circumferential speed around the black hole times the distance from the black hole. Relativistic laws state that this angular momentum stays the same along the Endurance’s trajectory. As the Endurance is moving toward Gargantua, the circumferential speed increases and distance decreases. The Endurance moves toward the black hole with a certain amount of energy. This energy consists of gravitational energy, centrifugal energy, and radial kinetic energy. Gravitational energy becomes more and more negative, centrifugal energy increases because circumferential motion is also increasing, and radial kinetic energy increases because motion is increasing. Critical orbit is the orbit around Gargantua that balances gravitational and centrifugal forces. This orbit is very unstable, and if you are on the inside of the critical orbit, gravity overwhelms centrifugal energy and you are pulled into the black hole. If you are on the outside of the orbit, centrifugal energy overwhelms gravity, allowing you to escape. The trajectory of the Endurance leads the ship too close to Gargantua, so Cooper uses Lander 1 and Ranger 2’s rockets to drive the ship out of Gargantua’s grip. For another push, Cooper detaches Lander 1 and Ranger 2, producing small explosions from the bolts. As the lander and ranger plunge toward Gargantua, the Endurance returns to critical orbit where CASE and Brand use a small rocket blast at the right time to send the Endurance to Edmund’s planet. (Thorne, 2014)

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