Could a star half as hot as our sun maintain similar surface temperatures of planets orbiting it if it was half the distance?

Question

I'm trying to build a world that is orbiting a red giant but sustains life similarly to the conditions of earth.Since red giants are about half the temperature (3000 kelvin) of our sun (6000 kelvin) life could not be sustained, at least not to the same extent. (I'm trying to keep the surface temperature about 20-60° Celsius)

Since red giants are about half the temperature of our sun, if it was half the distance away from the planet would the temperatures be the same? Assuming it's solar mass was 0.5 that of our sun as well, would there be an increase in gravity or would the planet be able to orbit normally with no adverse affects?

The closer proximity seems as though it would cancel out the lack of temperature, and the halving of mass would furthermore cancel out the increased gravity of the closer proximity.

Answer 1

It is not the surface temperature of a star, or not the surface temperature alone, that determines the distance that habitable planets orbit at.

The surface temperature determines how much energy the star emits per unit of surface area. The total surface area of the star multiplied by how much energy is emitted per unit of surface area gives the total energy emitted by the star.

If Star A emits four times as much energy as star B, a planet would have to orbit Star A at twice the distance as a planet orbiting star B in order to receive the same amount of energy.

A red giant star would not be dimmer than the Sun. Red Giant stars have very large surface areas and thus emit many times as much total energy as the Sun. Furthermore, the red giant phase is a relatively temporary phase in the life cycle of a star, and a planet that is at the right temperature for life to flourish on it while the star is a red giant will not remain at the right temperature for long enough for the life to develop interesting features.

You might want to make your planet orbit a dim red dwarf star instead of a vast red giant star.

The different aspects of stars do not have linear relationships but instead have geometric relationships. For example, a one percent change in the mass of a star will cause much more than a one percent change in the diameter, surface temperature, and total luminosity of the star.

Here are some links to sites that calculate the habitable zones of stars:

https://www.google.com/search?newwindow=1&q=habitable+zone+calculator&sa=X&ved=0ahUKEwjKsfe7oPDZAhXvYd8KHYInAU4Q1QII8QEoAQ&biw=1920&bih=9491