# How large are the various forces and torques that the Parker Solar Probe will experience during its closest flyby of the Sun?

The Parker Solar Probe will experience forces and torques as it passes within about 8.5 solar radii of the Sun's surface that even a General Products hull will not protect it from.

How large will the tidal acceleration be along the 3 meter length of the spacecraft at perihelion? Will it be detectable in any way?

Will there be any (real or effective) torques that will tend to rotate the spacecraft during it's closest flybys? What about effects due to the oblates of the sun?

Will any of these be a new record - or have Cassini or Juno experienced greater effects during their closes approaches to Saturn and Jupiter already? above: Parker Solar Probe cropped, from here. above: screen shot from NASA's Solar Probe Plus Fact Sheet note: the link seems to be dead now, but there is plenty of related information available at http://solarprobe.jhuapl.edu/index.php#spacecraft above: Illustration of Parker Solar Probe's orbit, from here.

• Solar corona density is about 10^15 particles per m^3, mostly hydrogen - that converts to 1.6x10^-12 kg/m^3. That corresponds to ~400km LEO altitude - atmospheric drag similar to that experienced by ISS, except at 195km/s instead of 7.6km/s. I bet all other effects will be overshadowed by this.
– SF.
May 31, 2017 at 12:12
• @SF. hey wait - which is moving faster, the spacecraft or the protons? If there is drag, will it be tangential or radial?
– uhoh
May 31, 2017 at 13:28
• Both (or diagonal). Solar wind is outwards, supposedly at 400km/s if I got the sources right - not sure if that's the state inside the corona, or just "out around here".
– SF.
May 31, 2017 at 13:30
• The probe will be moving along a ~200 km/s transverse to the solar radial direction and the solar wind speed varies between ~300–800 km/s depending on location and time. If we use the $10^{15} \ m^{-3}$ density and 600 km/s for the speed, we get a ram pressure of ~0.3 Pa. If we naively assume the spacecraft has 1 $m^{2}$ of surface area, then there will be ~0.3 N of force acting on it for the perihelion pass. PSP launched with a mass of ~685 kg, so it would experience an acceleration of 0.00044 $m \ s^{-2}$. Sep 2, 2018 at 13:11

The largest torque affecting the Parker Solar Probe during its closest approach is caused by the solar wind blasting against the heat shield (Thermal Protection System, a.k.a TPS).

The TPS is like an umbrella held facing into a strong wind. The wind whips against it, and tries to force it around away from the wind. The spacecraft has to "fight" against this force to maintain it's proper attitude with the TPS pointed right at the sun and right into the solar wind.

To "fight" against the solar wind, the primary mechanism is the spacecraft's reaction wheels. They are mounted at angles to each other (there are four) and they are spun up or slowed down to create the counter force to the solar wind acting on the TPS. The spacecraft subsystem that controls the wheels is the Guidance and Control (G&C) system. Fifty times a second (50 Hz) the inertial measurement unit provides change-in-attitude readings and the G&C system calculates the reaction wheel response required to counter act the change and bring the spacecraft back to the correct attitude with the TPS pointing at the sun.

In addition to controlling attitude with the reaction wheels, the spacecraft thrusters can also be used, but this is not normally done because it degrades the science measurements. However, as the reaction wheels counter the torques from the solar wind, they wind up and spin faster and faster. In order to bring the speed back down, the spacecraft periodically performs a "monmentum dump" by firing the thrusters to counter-act the wheel's momentum and allow them to slow down to a manageable rate.

• Great answer! When I asked this question I was also wondering about any subtle tidal effects, either Newtonian or due to general relativity, that could produce local forces and torques on the spacecraft and it's components. The effect is usually fairly small, but moving at such a high velocity in such a large gravitational gradient, will there be forces and/or torques due to these as well? I guess Larry Niven's short story Neutron Star made a big impression on me. (e.g. this question)
– uhoh
Jan 7, 2018 at 7:38
• Unfortunately, I am not knowledgeable enough of the basic physics to be able to answer that question from a theoretical point of view. From a practical point of view, I have never heard any of the spacecraft G&C team talk about or worry about such effects. This leads me to believe that, to the extent that they exist they are relatively (<- pun ) minor.Any and all torques, including mechanical impact from dust (as discussed in another answer) would be "summed up" into the IMU measurements and accounted for in that way. Jan 7, 2018 at 18:36
• OK, but "How large" appears in both the title and the body of the question. Can you post an approximate numerical value for the torques you do discuss?
– uhoh
Jan 8, 2018 at 8:02
• I can ask someone familiar with the G&C analysis if they can give some plausible numbers. Of course they would have to have a very good idea of the forces they are dealing with, but they also have to account for the "unknown unknown" by adding margin to all calculations and simulations. What they do is repetitive Monte Carlo simulations using a range of assumptions and random events. They run these over and over to test the various scenarios against their design and algorithms and make various tweaks. I'll see what they say. Jan 9, 2018 at 1:19
• Congrats on Parker's success so far btw!
– uhoh
Dec 6, 2018 at 0:23

The other answer suggests that ram pressure is the dominant effect on the spacecraft. I messed this up in my first thoughts on the problem too, but it's actually radiation pressure from sunlight.

On it's latest perihelion pass, Parker Solar Probe (PSP) passed within ~13.3 $$R_{s}$$ of the Sun and had a maximum speed relative to the Sun of ~160 km/s. The particle number density topped out at ~8000 $$cm^{-3}$$. The solar wind speed relative to the spacecraft topped out around ~600 km/s (excluding a few peaks up to ~800 km/s for very short intervals). All of this adds up to a ram pressure of ~2.41 $$\mu$$Pa (even if I used the 800 km/s peaks, it would increase this by less than a factor of 2). The solar wind near Earth typically has number densities around 10 $$cm^{-3}$$ and speeds around 400 km/s, or ram pressures of ~0.0013 $$\mu$$Pa, or about 3200 times smaller than at ~13.3 $$R_{s}$$.

The Sun's luminosity is ~$$3.828 \times 10^{26}$$ W, so at one astronomical unit (AU) (~214.94 $$R_{s}$$) the power per unit area is ~1361 W $$m^{-2}$$. At ~13.3 $$R_{s}$$ the solar power per unit area is ~355,500 W $$m^{-2}$$, or an increase by a factor of ~261.

PSP's heat shield has a radius of ~4 ft (~1.2192 m). If we approximate it as a circular disk, then its area would be ~4.6698 $$m^{2}$$. The force from radiation pressure is given by: $$F_{rp} = \frac{ L_{s} }{ 4 \ \pi \ r^{2} \ c } \ C_{r} \ A_{abs} \tag{0}$$ where $$L_{s}$$ is the solar luminosity given above, $$r$$ is the radial distance from the Sun's center, $$c$$ is the speed of light in vacuum, $$C_{r}$$ is the coefficient of reflectivity, and $$A_{abs}$$ is the absorbing area.

If we divide both sides by $$A_{abs}$$ we get a solar radiation pressure, $$P_{rp}$$, exerted on whichever area is of interest. In this case, it's the heat shield. Throwing in the numbers for $$r$$ ~ 13.3 $$R_{s}$$, we get $$P_{rp}$$ ~ 1185.8 $$\mu$$Pa, or nearly 500 times that of the ram pressure given above.

In regards to the other answer given before mine, the reaction wheels are necessary to make sure the heat shield always points at the Sun and keeps all necessary equipment in shadow. This is absolutely essential as several instruments in shadow were not designed to handle the solar radiation fluxes that will be experienced at it's closest approach of ~9.5 $$R_{s}$$. In fact, the thermal conductivity of many of the parts in shadow are so high that were the whip antenna at the tail of the magnetometer boom to be exposed to sunlight, it would ablate in a few 10s of seconds and start to over heat the magnetometer sensors. This would also drastically change the spacecraft's moment of inertia, which would throw the automated attitude corrections into a state of confusion. There are lots of checks to try and mitigate scenarios like this one but the worst case is that the attitude keeps turning the reaction wheels under the assumption the spacecraft is whole. This will be insufficient and the spacecraft will continue to rotate such that more and more of the side is exposed to sunlight. The end result would be that the heat shield would come flying out on the other side of perihelion alone, the rest of the spacecraft bus would be completely ablated.

• Wow, fascinating! How much change is "drastically"? Would the magnitude of the change in spacecraft moment of inertia due to catastrophic ablation loss of the whip antenna be more than 1%? I'd always thought that attitude control systems were based at least partly on feedback rather than "If I do this, the attitude will be correct, no need to check my assumptions nor to see how well it's working." Am I misunderstanding what you're describing in the last paragraph?
– uhoh
Jan 4 at 20:45
• @uhoh - There are star trackers and sun sensors on the spacecraft that try to keep the sunshield pointed at the Sun. They've screwed up in the past at Venus because the spacecraft thought Venus was the Sun. That comment was based upon discussions I had with the mission scientist before launch. The long mag boom can affect the moment of inertia quite a bit, but I don't recall precisely. I just recall him saying it would be enough (were mitigations not taken) to screw up attitude and cause a fatal loss of the bus. I assume mitigations were taken... Jan 4 at 21:44