How to Be an Orbital Mechanic: Reading Orbit Plots with Parker Solar Probe

By Dr. Tom Bridgman
NASA’s Goddard Space Flight Center

On Oct. 29, 2018, at about 1:04 p.m. EDT, Parker Solar Probe became the closest spacecraft to the Sun, breaking the record of 26.55 million miles from the Sun’s surface set by the Helios 2 in April 1976. But this is just the beginning. Parker Solar Probe — NASA’s mission to touch the Sun — will get closer still.

This process is the result of carefully planned orbital mechanics, which will result in 24 passes around the Sun. Parker starts off in an orbit around the Sun which is the same as Earth’s – that’s where it starts, after all – and gradually moves to a position inside the orbit of Mercury.  To do this, the spacecraft must slow down significantly (see Figure 1).

Figure 1: Parker Solar Probe orbit in the plane of the solar system. Parker orbit data from JHU Applied Physics Lab. Solar system orbit data from JPL/NAIF.

One of the fundamental principles of orbital dynamics is that if you want to change the periapsis, or point of closest approach, of an elliptical orbit, you get the most bang for your buck if you change speed at the apoapsis, or the point when you’re furthest away.

You can see this principle applied in the case of Parker Solar Probe. Figure 2 below plots Parker’s orbital velocity on the y-axis (how fast it’s moving relative to the Sun, in kilometers per second, km/s), with time plotted along the x-axis. Parker is represented by the purple curve; Mercury (black curve) and Earth (blue curve) are included for reference. [Click on the graph to see a full-size version.]

Figure 2: Parker Solar Probe orbit speed plotted with inner solar system planets for comparison. Parker orbit data from JHU Applied Physics Lab. Solar system orbit data from JPL/NAIF.

The first thing you’ll notice is that the purple line is moving up and down quite a bit, indicating changes in its orbital velocity: Parker doesn’t travel at a constant speed throughout its orbit, but rather speeds up and slows down at different points.

The little dots that appear at the spikes and the dips on the curve mark the times when Parker is either furthest from or closest to the Sun on each orbit. The aphelion positions, when Parker is farthest away from the Sun, are marked with red dots: Note that they coincide with the dips in the curve, when Parker has its slowest speed. The perihelion, or close approaches, are marked with green dots, and coincide with the spikes in the graph, where Parker is traveling fastest.

Over time, you can see that the spikes get taller: Parker’s speed at perihelion gets faster and faster.  Although the graph doesn’t directly show this, these increases in speed correspond to Parker’s perihelion moving closer and closer to the Sun: The closer it gets, more of the Sun’s gravitational energy gets translated into the spacecraft’s energy of motion, increasing its speed.  Parker launched from Earth orbit with a speed of about 17 kilometers per second (38,000 miles per hour), slower than the orbital speed of Earth (about 29 kilometers per second or 65,000 miles per hour), enabling it to ‘fall’ towards the Sun.  Accelerating in the Sun’s gravity, it reached a speed of over 95 kilometers per second (212,000 miles per hour) at the first closest approach.  But looking at the graph, we see that Parker will go faster (and closer) still, its final orbit approaching over 190 kilometers per second (425,000 miles per hour).

But how does Parker keep getting closer?  Getting closer to the Sun doesn’t come for free — each shift in the orbit requires the help of gravitational assists from Venus.  Note on the graph above that every time the spacecraft transitions to a higher speed at perihelion, or spike in the curve, there is a prior speed decrease near aphelion, or the dip in the curve, marked on the plot by a thicker red line. For Parker, these speed changes are accomplished with fly-bys of the planet Venus near Parker’s aphelion position. Unlike many gravity assists where spacecraft gain energy from sling-shotting around a planet, Parker is losing energy to Venus in order to slow down. By slowing down at aphelion, the orbit’s overall size decreases, which in turn increases the spacecraft’s speed near the Sun.

Parker doesn’t fly by Venus on every single orbit, it will only go past the planet seven times over the course of seven years – but you can spot the flybys in the graph by noticing a small jag in certain spots. If Parker is accelerating towards the Sun — i.e., on the upward slopes in the graph, after the dip in a curve — the flyby appears as a little jag in the orbit, like the one just after October 2019 and October 2021. However, some flybys occur while the spacecraft is outbound from the Sun and decelerating, like the one near July 2020, which is a little less obvious in the plot.  Each jag represents Parker moving just a bit slower, just a bit closer to the Sun – on each orbit gathering unprecedented, in situ observations of the star we live with.