This isn't exactly an answer to the question as asked, but it's close enough to one that you might find it interesting and hopefully helpful in some way.
The gravitational force of the Sun on the Earth is given by
$$F_{Grav} = \frac{GM_{Sun} M_{Earth}}{a^2}$$
where $a$ is the semimajor axis of Earth's orbit and is about 1.5E+11 meters and $GM_{Sun}$ is the standard gravitational parameter of the Sun, or about 1.327E+20 m^3/s^2. The mass of the Earth is about 5.97E+24 kg.
The force due to radiation pressure of the Sun's light on the Earth can be estimated as
$$F_{Rad} = Area_{Earth} \frac{I_{Sun}}{c} = \pi R_{Earth}^2 \frac{I_{Sun}}{c} $$
where the mean radius of the Earth $R_{Earth}$ is about 6.37E+06 meters and the intensity of sunlight on the Earth $I_{Sun}$ is roughly the solar constant ($G_{SC}$) and is about 1361 Watts/m^2.
The ratio of the two
$$\frac{F_{Rad}}{F_{Grav}} = \frac{\pi R_{Earth}^2 I_{Sun} a^2}{c \ GM_{Sun} M_{Earth}} $$
That ratio is about 1.6E-14, which is pretty small!
If we somehow made the surface of the Earth darker or lighter with different distributions across the planet versus time of year and time of day, we could (i.e. changing Earth's visible light albedo) we could play tricks with its orbit.
For example, if we reflected more daylight westward (prograde) than eastward (retrograde) throughout the year, we could over billions of years bring Earth's average orbit ever-so-slightly closer to the Sun. Of course changing Earth's visible light albedo would have dramatic and Earth-changing heating and cooling effects on the Earth, but that's a different story.
We could also flip that around every six months in order to circularize our orbit and keep us a more constant distance from the Sun, but as @JamesK's answer points out it's cold in one hemisphere (and warm in the other) because of the tilt of Earth's axis, not because of the change in distance from the Sun.