Spacecraft Gravity Assist by Planet

Propellant for probes to other planets in our solar system can be greatly reduced by use of close flybys of planets. The main reason for this is that the planet has a lot of orbital speed so that, when the spacecraft is under its gravitational force influence, the planet tends to make a component of the spacecraft's velocity equal to its own orbital speed. This effect is explored by this animation. In this animation, the un-propelled spacecraft is represented by the blue circle and the planet is represented by the red circle. It is assumed that the ratio of mass of the spacecraft to that of the planet is so small that the planet does not change speed as the spacecraft flies by. But the spacecraft can increase its speed by as much as the difference between the planet orbital speed and the initial spacecraft speed. The planet always starts at coordinates `(x,y)=(0,0)` and moves downward at the adjustable `v_y`. The learner has access to initial velocity of the spacecraft, as well as its initial `(x,y)` coordinates. The learner can also choose the factor `GM` where `G` is the gravitational constant and `M` is the planet's mass. Then if `r` is the distance between centers of planet and spacecraft, `(GM)/(r^2)` is the magnitude of the spacecraft's acceleration at any r. We can obtain the incremental changes of spacecraft velocity from this acceleration and from the total velocity we can obtain the position of the spacecraft. These are the results of this animation.

Usually the passage through a planet's gravity influence will change the direction of the spacecraft's velocity. As shown in the link, this course change can be corrected with very little expenditure of energy by use of thrusters that are directed normal to the current velocity. Course restoration is a checkbox option that can be chosen.

Course correction has another big benefit especially for trajectories that would have been bound to the planet: It gets the space craft far away from the gravity of the planet as quickly as possible so that its slowing due to gravity is minimized. One of the obvious outcomes of this endeavor can be a trajectory where the spacecraft effectively gets bound in an orbit around the planet.

To an observer on a fixed frame of reference this will look like an N-shaped trajectory where the spacecraft makes repeated close encounters with the planet. This type of trajectory must and can be avoided by choosing more appropiate initial conditions. After any change of parameters, the program prints out the eccentricity, e, of the expected trajectory. If e>1 then the trajectory will not be or the bound type. Even if e<1, if course restoration is used, then velocity can be gained from the encounter with the planet. An obvious pitfall that can occur with certain choices of parameters is that the spacecraft can go too close to or crash into the planet. If it goes too close, the acceleration due to gravity gets too large and the resulting trajectory will have large errors. If that happens, the learner may change parameters appropriately so the the flight doesn't get so close to the planet. The learner may also set a minimum distance, sMin, below which the current simulation will abort and ask the learner to set new initial parameters. When course restoration is chosen, the program prints out the specific energy (energy per unit mass) used to correct the course. This energy is to be compared with the square of the initial velocity and is usually only a few percent of that.