I can't speak to the astrological consequences of a planet being in retrograde, but I can tell you about the gravitational effects thatit might have. (TLDR: not much, but calculable).
First I’ll define some terms and introduce some physics, then I’ll show the calculations and results, then I’ll compare those to some other values to put things in perspective.
If you watch a clear sky over the course of a day and night, you’ll see the Sun, Moon, stars, and planets rise in the East and set in the West.(1) However, when you look at the sky from one night to the next, the Sun, Moon, and planets appear to move relative to the stars. Most of the time, they all seem to be moving Eastward relative to the stars. This is known as “prograde”. Occasionally, the planets appear to move in the opposite direction, Westward relative to the stars. This is known as “retrograde”.
Now that we understand that the Sun (rather than the Earth) is near the center of our solar system, we’re able to explain why this happens. Planets closer to the Sun move through their orbits faster, both in angle and by speed. When an inner planet (Mercury or Venus) passes by the Earth, it seems to move backwards. When an outer planet (Mars, Jupiter, Saturn, Uranus, or Neptune) is passed by the Earth, they seem to move backwards. One place to find a nifty simulation of all of this (with additional explanatory pages) is here.
Our understanding about forces and gravity changed a lot about a hundred years ago, but as far as forces from the planets go, Newton’s laws from the seventeenth century work just fine. Newton’s law of universal gravitation tells us that the force of gravity between two objects is always attractive, drops off with the square of the distance between the centers of mass of those objects, and is proportional to the product of those masses. Written as an equation this is:
F(gravity) = G* m1 * m2/(r^2)
where:
F(gravity) = gravitational force
G = the universal gravitational constant (6.673 x 10^-11 N*m^2*kg^-2)
m1 = mass 1
m2 = mass 2
r = distance between the center of mass of m1 and m2
Newton’s second law of motion tells us that the total force acting on an object is equal to that object’s mass multiplied by that object’s acceleration. Written as an equation, this is:
F(total) = m*a
Combining these two relationships we have:
F(gravity) = F(total)
G*m1*m2/(r^2) = m2 * a
G*m1/(r^2) = a
If no other force were acting on object #2, it would accelerate towards object #1 at a rate of G*m1/(r^2). If we find out how large this amount is, we can multiply it by the mass of any object #2, and find out the size of the force acting on it.
The direction of apparent motion of the planet doesn’t directly determine the size of the force acting from it. The distance to the planet does. However, other planets are also closest to the Earth when they are undergoing retrograde motion, and furthest during prograde. The size of the force changes gradually throughout the orbit, but we could look at the extremes. If you use the data in the table below (2) then we see that largest differences in acceleration between retrograde and prograde positions are quite small.
For Mercury, this is about 3 billionths of a meter/(second squared), or about 200 billionths of a newton (50 billionths of a pound) of force on a 70 kg (150 lb.) adult. Jupiter produces the largest force and acceleration ranges between its furthest and closest approaches of about 150 billionths of a meter/(second squared), or about 10 millionths of a newton (2.3 millionths of a pound) on a 70 kg adult.
The Moon, which doesn’t undergo retrograde motion, produces a larger range of forces still, between the extremes of its position, ignoring the size of the Earth itself (which can’t if we are looking at tides, a topic for another time) this is about 7 millionths of a meter/(second squared) or about 500 millionths of a newton (100 millionths of a pound).
The internet informs me, however, that the range of g, the gravitational field strength of the Earth, at Earth’s surface, extends from 9.7639 m/s^2 to 9.8337 m/s^2. This means that a 70 kg adult would vary in weight by about 5 newtons (about 1 pound)depending on where on the Earth they stand. These differences, while small, are millions of times larger than the range of gravitational forces we experience from the planets. In fact, they are so small, that the force of gravity between two 70 kg adults standing 10 cm (4 inches) apart is about the same strength (30 millionths of a newton) as the largest of the ranges of forces one might experience from the planets.
(1) In general. Most stars will be rising somewhat North or South of East and setting somewhat North or South of West. Also, if you’re in the Northern hemisphere, some amount of the stars will appear to revolve counter-clockwise about a point near the North Star without crossing the horizon, and in the Southern hemisphere, some amount of the stars will appear to revolve clockwise about a different point in the sky. When you’re closer to a pole than the Arctic or Antarctic circles, the Sun, Moon, and planets also might not cross the horizon depending on the time of the year.
(2)
Aphelion = the largest distance an object is from the Sun.
Perihelion = the smallest distance an object is from the Sun.