How bright would Alpha Centauri appear (in apparent Magnitude) if it were 1 light year away? I'm trying to determine what a star of comparable mass and luminosity to the Sun would look like from the surface of the Earth if it were 1 light year away - I chose Alpha Centauri since it is close to us, and similar to the Sun. Could a star like the Sun be that close without exerting significant influence over it, or would they have an orbital relationship? I'm trying to design a star system for a science fiction novel, and would like there to be a star close enough and bright enough to be visible during the day, and cast a shadow at night, but far enough away to provide no heat energy, and be free from the Sun's gravity.
The change in magnitude is given by:
$$m_2-m_1=-2.5\ \log_{10}(B)$$

Where B is the change in brightness.

Alpha Centauri is about 4.4ly so inverse square says it would be 19.4x brighter at 1ly, so a magnitude differential of -3.2.

Its apparent magnitude would therefore go from -0.27 to -3.47. This is brighter than Sirius (-1.46) but not close to the Sun (-26.7) nor Venus. Venus doesn't cast a shadow, so neither would Alpha Centauri at 1ly.

On gravity, Jupiter is roughly one thousandth the mass of Alpha Centauri but would be about 63,000x closer than the star at 1ly. It would therefore have a gravitational effect on the Sun of:
$$63\,000^2/1000=\mathrm{4\ million\ times}$$
that of Alpha Centauri at 1ly!

Sounds like this works for your story.

Data brightness sources: https://www.space.com/21640-star-luminosity-and-magnitude.html

Mass and distance sources: https://en.wikipedia.org