<p>I have a theoretical problem that merges the effects of a gravitational field and the Sun radiation pressure. The problem goes as follows:</p>
<blockquote>
<p><em>A spacecraft orbits the Sun in absence of any other body interaction. The spacecraft surface is not negligible compared to its mass and it
faces the Sun with the same orientation at all times. Does the
trajectory satisfy the conditions of a Keplerian motion (i.e. is the
trajectory a conic section?) Same question when the Sun is not a
sphere but a flat disc whose axis is pointing always in the direction
of the spacecraft.</em></p>
</blockquote>
<p>My answer is that in both cases we can consider that the spacecraft will move in a conic section. If you consider that SRP is always acting in the opposite direction of the gravitational pull of the Sun, both forces would form a central vector force field, where the gravitational force would be decreased by the SRP. If the motion described by the S/C only considering gravity is a conic section I do not see any reason why it should be different in that case.</p>
<p>For the case of the Sun as a flat disc, considering that it would be pointed always to the S/C, the force is again central (although the potential would not be circular).</p>
<p>I have not found a better explanation for this, although I feel there is some kind of theoretical insight that I might be missing.</p>
<p>Thanks for the help!</p>

CC BY-SA 4.0
2021-02-04T22:02:39.380Z
For circular orbits, the SRP force will be perpendicular to the velocity vector of the spacecraft, so the angular momentum won't change.  For highly elliptical initial orbits, the case will be more complicated since the SRP force will now be only perpendicular to velocity at aphelion and perihelion. My intuition is that it will slowly circularize the orbit, but it won't be Keplerian until it is circularized (or crashes). Related: https://physics.stackexchange.com/questions/70357/change-of-orbit-with-radial-impulse
Connor Garcia
CC BY-SA 4.0
2021-02-04T22:14:52.077Z
@ConnorGarcia
 Quoting from the answer you posted:
"The net effect of the constant radial force is equal to a local change in the attractive gravitational force. And since gravity is a conservative force, there can be no net gain in energy."
However, he explains that there would be an in-plane offset, which I do not find reasonable. The net effect is that you are reducing the influence of the gravitational pull exerted by the Sun, or Earth. Considering equilibrium conditions (and not transitory effects) the S/C would move as if it was under the influence of a less massive body.
SERGI LÓPEZ
CC BY-SA 4.0
2021-02-04T22:26:59.950Z
I only posted the other answer as related, but not quite the same question.  I don't think there will be a in-plane offset for your question since presumably SRP forces were in effect as the spacecraft was inserted in it's initial orbit and outward radial force wasn't instantly imposed at some time.  For your question, I agree that the S/C would move as if under the influence of a less massive body (for a circular orbit).  It is certainly not the case that the S/C would move as if it were under the influence of a less massive body if the orbit was significantly eccentric.
Connor Garcia
CC BY-SA 4.0
2021-02-05T05:23:04.613Z
*"it faces the Sun with the same orientation at all times."* So the SRP force will always be proportional to the gravity (since they both obey the inverse square law). And the spacecraft is rotating on its axis, with the rotation period equal to its orbit period. But if the eccentricity is >0 then it can't rotate with constant angular momentum, the rotation angle has to keep pace with the orbit's true anomaly, not the mean anomaly.
PM 2Ring
CC BY-SA 4.0
2021-02-07T10:24:36.833Z
Sorry but where does it say anything about radiation pressure in the formulation of the problem? To me it is asking whether a rotation of the satellite and/or a non-spherical central mass would affect the orbit.
Thomas
CC BY-SA 4.0
2021-02-08T12:34:32.257Z
It does say that it has a surface non negligible with its mass, i.e. SRP is a force that should be taken into account. As for the angular motion of the satellite, if we consider it a point mass, the SRP will not change the angular momentum of the orbit, as it acts through the position vector (dh/dt=r X F). The force field would be also conservative as it would only depend on the distance from the S/C to the Sun.
SERGI LÓPEZ
<the-sun><orbit><orbital-mechanics><mathematics>
Classical Mechanics : Interaction Sun Radiation Pressure - Gravitation
SERGI LÓPEZ
# Classical Mechanics : Interaction Sun Radiation Pressure - Gravitation

(Asked by: username_0 on 2021-02-04)

I have a theoretical problem that merges the effects of a gravitational field and the Sun radiation pressure. The problem goes as follows:

> *A spacecraft orbits the Sun in absence of any other body interaction. The spacecraft surface is not negligible compared to its mass and it
> faces the Sun with the same orientation at all times. Does the
> trajectory satisfy the conditions of a Keplerian motion (i.e. is the
> trajectory a conic section?) Same question when the Sun is not a
> sphere but a flat disc whose axis is pointing always in the direction
> of the spacecraft.*

My answer is that in both cases we can consider that the spacecraft will move in a conic section. If you consider that SRP is always acting in the opposite direction of the gravitational pull of the Sun, both forces would form a central vector force field, where the gravitational force would be decreased by the SRP. If the motion described by the S/C only considering gravity is a conic section I do not see any reason why it should be different in that case.

For the case of the Sun as a flat disc, considering that it would be pointed always to the S/C, the force is again central (although the potential would not be circular).

I have not found a better explanation for this, although I feel there is some kind of theoretical insight that I might be missing.

Thanks for the help!

**Tags:** the-sun, orbit, orbital-mechanics, mathematics
> **Comments:**
> **username_1**: For circular orbits, the SRP force will be perpendicular to the velocity vector of the spacecraft, so the angular momentum won't change.  For highly elliptical initial orbits, the case will be more complicated since the SRP force will now be only perpendicular to velocity at aphelion and perihelion. My intuition is that it will slowly circularize the orbit, but it won't be Keplerian until it is circularized (or crashes). Related: https://physics.stackexchange.com/questions/70357/change-of-orbit-with-radial-impulse  
> **username_0**: @ConnorGarcia  Quoting from the answer you posted: "The net effect of the constant radial force is equal to a local change in the attractive gravitational force. And since gravity is a conservative force, there can be no net gain in energy." However, he explains that there would be an in-plane offset, which I do not find reasonable. The net effect is that you are reducing the influence of the gravitational pull exerted by the Sun, or Earth. Considering equilibrium conditions (and not transitory effects) the S/C would move as if it was under the influence of a less massive body.  
> **username_1**: I only posted the other answer as related, but not quite the same question.  I don't think there will be a in-plane offset for your question since presumably SRP forces were in effect as the spacecraft was inserted in it's initial orbit and outward radial force wasn't instantly imposed at some time.  For your question, I agree that the S/C would move as if under the influence of a less massive body (for a circular orbit).  It is certainly not the case that the S/C would move as if it were under the influence of a less massive body if the orbit was significantly eccentric.  
> **username_2**: *"it faces the Sun with the same orientation at all times."* So the SRP force will always be proportional to the gravity (since they both obey the inverse square law). And the spacecraft is rotating on its axis, with the rotation period equal to its orbit period. But if the eccentricity is >0 then it can't rotate with constant angular momentum, the rotation angle has to keep pace with the orbit's true anomaly, not the mean anomaly.  
> **username_3**: Sorry but where does it say anything about radiation pressure in the formulation of the problem? To me it is asking whether a rotation of the satellite and/or a non-spherical central mass would affect the orbit.  
> **username_0**: It does say that it has a surface non negligible with its mass, i.e. SRP is a force that should be taken into account. As for the angular motion of the satellite, if we consider it a point mass, the SRP will not change the angular momentum of the orbit, as it acts through the position vector (dh/dt=r X F). The force field would be also conservative as it would only depend on the distance from the S/C to the Sun.  

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