# Why does Starman/Roadster have radial acceleration?

Discussion in chat pointed out that the SpaceX Roadster or Starman has a Marsden A1 coefficient.

From solution 10 in Horizons:

 EPOCH= 2458164.5
EC= .2585469914787243  QR= .9860596231806226  TP= 2458153.620483722645
OM= 317.3549094214575  W = 177.3203028023227  IN= 1.088451292866039
A1= 2.960683526738534E-9  R0= 1.  ALN= 1.  NM= 2.  NK= 0.
SRC= -2.057839421666802E-7...


I wrote about the Marsden parameters in this question a while ago and have linked several sources there. You have to use that in a certain power-law equation and use units of days and AU, so A1 is 2.96E-09 AU/day^2.

Question: Why does Starman/Roadster have radial acceleration? What is causing this? Can the size of the acceleration be understood quantitatively?

Aliens are trying, very slowly, to steal it?

Air leaking out of the tires?

## 1 Answer

Sunlight pressure. The acceleration is 9.08 μN / m2 (Assuming perfect reflectivity). The size is about 3.66* 12.6 = 46 m2. That gives a thrust of about 414 uN. The mass is about 1300 kg. Thus the acceleration from sunlight max is about 3.2 e-7 m/s2. Of course, there are a lot of assumptions in that, the mass is probably higher, it won't be perfect reflectivity, and a good part of that time not all of it will be pointed in the correct direction, still, this is a fair estimate. The acceleration will also vary as one gets further from the Sun.

The units for A1 from Horizons are actually AU/day2, and are subject to a very complex formula. That changes to 5.93321266 × 10-8 m/s2. It is even more complex than that, however, the actual acceleration depends on the distance from the Sun. Lucky for us, the numbers I calculated assume 1 AU, and at that point they are nearly identical. So that is a reasonable approximation, and this value is perfectly consistent with a low reflective pointing mostly away from the Sun Starman.

• 46 m^2, not m^s. – Skyler Mar 4 '19 at 19:54
• Doesn't the solar wind also provide some outward pressure? – Loren Pechtel Mar 5 '19 at 5:54
• @LorenPechtel: Yes, but negligibly weak comparing to light pressure. – SF. Mar 5 '19 at 10:27