Astro2110 – The Solar System

So far, there are several hypotheses about the formation of the earth and the solar system. There are two main popular hypotheses: one believes that the solar system was produced by a violent accidental mutation, the catastrophe theory; the other believes that the solar system evolved gradually in an orderly manner, that is, evolutionary theory.

In 1755, the German philosopher Kant proposed the hypothesis of the formation of the solar system based on Newton’s principle of universal gravitation. He believed that the sun, planets, and moons in the solar system formed gradually from nebulae—thin clouds of granular matter. In 1796, French astronomer Laplace also proposed a nebula theory similar to Kant’s. Later generations often combine the two together, collectively referred to as “Kant-Laplace nebula theory”. This assumption dominated most of the 19th century.

Scientists believe that stars form as spherical fragments of a primordial nebula that runs through the Milky Way. Under the action of its own gravity, it constantly shrinks and creates a vortex. The vortex shattered the nebula into a multitude of fragments, each of which gradually transformed into a star. The sun is one of them, and it is also constantly shrinking and rotating, forming the original sun in long-term motion. The surrounding objects continue to gather, collide, and become larger and larger, forming today’s eight planets. The material around the planets also gradually formed moons in this way. This is one of the leading hypotheses for the formation of the solar system.

In Andy Weir’s The Martian, NASA plans to send a supply probe to Mars to save the stranded astronaut Mark Watney through what’s called the ‘Hohmann Transfer Orbit‘. What exactly is the Hohmann transfer orbit? And when the carrying capacity of rockets is limited, why does a probe following this orbit saves limited and precious fuel?

This maneuver is proposed by German scientist Walter Hohmann in his 1925 book The Attainability of Celestial Bodies. This orbital maneuver requires two thrusts to bring a probe from a lower orbit to a higher orbit (see Figure 1 below). The initial thrust is Δv, which is preferably applied when the probe is at its periapsis (lowest point of its orbit). This initial thrust raises the apoapsis (highest point) of its orbit, and sends the probe to an elliptical transfer orbit. The second thrust Δv’ raises the periapsis of its orbit, allowing the probe to match and enter the desired, higher orbit.

If we wish to let the probe intercept an object at the higher orbit (in our case Earth and Mars), we have to take the relative positions of Earth and Mars, and the typical travel time of the transfer into account. For Earth and Mars, the window for the Hohmann transfer opens once every 26 months, and a spacecraft following this orbit takes 9 months to reach Mars.

Hohmann transfer orbits are typically applied when the amount of fuel a spacecraft can take is limited. If time is of the essence, a probe can reach Mars much faster if it is capable of producing more thrust. In reality, the Hohmann transfer orbit requires less thrust when considering the gravitational effects of the planets at the initial and final positions, as maneuvering through the gravitational well of a planet conserves momentum and saves fuel. Also, the Hohmann transfer orbit can be applied backwards, sending a spacecraft to a lower orbit around a common central object by reversing the direction of the thrust.

I am excited to see how space agencies will apply this maneuver when we decide to send people to Mars! Here are some links to the Hohmann transfer orbit and the Oberth effect (powered flyby).