113 lines
4.5 KiB
Markdown
113 lines
4.5 KiB
Markdown
---
|
|
title: Solar radiation pressure
|
|
tags: radiation-pressure, srp, sun-synchronous, photon, area-to-mass
|
|
summary: The acceleration a sunlit surface receives from photon momentum, why it is a century scale effect rather than a perturbation, and how it shapes a constellation.
|
|
---
|
|
|
|
# Solar radiation pressure
|
|
|
|
A satellite is a body held together, not a body falling. The force that keeps
|
|
a small object from accelerating away, or from being pulled back in, is the
|
|
momentum carried by the light it reflects and absorbs. It is usually ignored
|
|
in a low Earth orbit model and dominant in a high one.
|
|
|
|
## Definition
|
|
|
|
**Solar radiation pressure** is the momentum flux carried by sunlight at a
|
|
distance `r` from the Sun. It is not a force on a satellite but on the light
|
|
it intercepts; the acceleration the satellite feels is the flux multiplied
|
|
by the satellite's area-to-mass ratio and by a reflectivity factor.
|
|
|
|
The pressure at one astronomical unit is about `4.56e-6 N/m^2`. Divided by
|
|
the area-to-mass ratio of a spacecraft, it gives an acceleration of the same
|
|
order as `J_2` on a large satellite at low altitude.
|
|
|
|
## Mathematics
|
|
|
|
### The flux
|
|
|
|
The flux falls as the inverse square of the distance,
|
|
|
|
$$
|
|
P(r) = P_{1\,\text{au}} \left( \frac{1\,\text{au}}{r} \right)^2
|
|
$$
|
|
|
|
with `P_1au = 4.56e-6 N/m^2` for total solar irradiance at 1 au.
|
|
|
|
### The acceleration
|
|
|
|
For a satellite with projected area `A`, mass `m`, and a coefficient
|
|
`C_R` that is 1 for absorption, 2 for perfect reflection and between for a
|
|
typical surface, the acceleration is
|
|
|
|
$$
|
|
a_{\text{srp}} = C_R \frac{P_{1\,\text{au}} A}{m} \left( \frac{1\,\text{au}}{r} \right)^2
|
|
$$
|
|
|
|
The `A/m` ratio is the whole story. It ranges from about `0.002 m^2/kg` for a
|
|
large communications satellite to about `0.05` for a small cube of a
|
|
CubeSat, a factor of 25 that is entirely attributable to structure.
|
|
|
|
### Three components
|
|
|
|
The acceleration along the Sun-satellite line has three distinguishable
|
|
parts, because the force acts where the light strikes:
|
|
|
|
- A **constant radial component**, which slightly lowers the effective
|
|
gravitational parameter and is absorbed into it.
|
|
- A **transverse component** along the orbit normal or the velocity
|
|
direction, which produces a secular change in the mean motion, that is in
|
|
the semi-major axis.
|
|
- A **short-period variation** with the orbital period, because the geometry
|
|
changes over an orbit when the satellite has a nonzero area ratio.
|
|
|
|
Only the middle one changes the orbit over time; the first is a constant and
|
|
the third averages out.
|
|
|
|
### Eclipse
|
|
|
|
In eclipse the satellite receives no radiation pressure. The effect is a
|
|
periodic reduction of the transverse acceleration, which produces a
|
|
cyclical variation in semi-major axis with the eclipse season rather than the
|
|
orbit, and it is why a radiation pressure constant is calibrated from the
|
|
mean over a long arc.
|
|
|
|
## Unit conventions
|
|
|
|
- Flux in watts per square metre; `P_1au = 1361 W/m^2` for total solar
|
|
irradiance, which corresponds to the pressure above.
|
|
- Area-to-mass ratio in square metres per kilogram.
|
|
- Distances in kilometres; the `1 au` ratio is dimensionless so the unit
|
|
does not matter there, but the acceleration that results must be in
|
|
kilometres per second squared to be consistent with the orbit.
|
|
|
|
## Applicability
|
|
|
|
The effect is a century-scale concern in the semi-major axis. For a high
|
|
Earth orbit with a large area-to-mass ratio, the semi-major axis drifts
|
|
noticeably over a few years, which is why the planning of a constellation in
|
|
the geosynchronous or high Earth orbit includes radiation pressure in its
|
|
station-keeping budget. For a low Earth orbit it is a perturbation beside
|
|
`J_2` and atmospheric drag.
|
|
|
|
The mean motion acceleration from the transverse component is what a model
|
|
should capture. The short-period term is smaller than it looks because it
|
|
averages, but for a sun-synchronous orbit it is not a perturbation at all,
|
|
because it is the mechanism: the nodal rate is chosen by tuning it against
|
|
`J_2`, and the two balance.
|
|
|
|
The eclipse term matters only where the radiation pressure is large, and it
|
|
matters because it is biased rather than symmetric.
|
|
|
|
## Standards
|
|
|
|
- Solar irradiance: IAU 2015 Resolution B3
|
|
- The pressure and flux conversions follow that resolution
|
|
- The effect as modelled in practice is described in Vallado,
|
|
*Fundamentals of Astrodynamics and Applications*
|
|
|
|
## See also
|
|
|
|
- [[perturbations]] for the size of the effect beside `J_2` and drag
|
|
- [[atmospheric-drag]] for the other century-scale term
|
|
- [[constellations]] for why a sun-synchronous plane is chosen by balance |