Expert: Philip A. Stahl - 4/1/2007

Question
how far from the sun's core would you need to be to get 1.1 to 0.9 times Earth gravity? is this out side of the corona? what is the radius of the sun and its parts?

Answer
Hello,

One can obtain the surface gravity of the Sun (at the photosphere - needed as a reference level) by using:

g =  GM / R^2

where G denotes the Newtonian gravitational constant:

G = 6.67 x 10^-11 N-m^2/ kg^2

M is the solar mass or M = 1.99 x 10^ 30 kg

and R is the solar radius:

R =  6.96 x 10^8  m

then we find,

g (Sun) =

(6.67 x 10^-11 N-m^2/ kg^2) (1.99 x 10^30 kg)/ (6.96 x 10^8 m)

or  g (Sun) = 274 m/s^2

compared to the Earth's surface gravity (average) of 9.81 m/s^2

Thus, at the solar photosphere, the Sun's surface gravity is already some 27.9 the Earth's.

To get "1.1 to 0.9 times Earth's gravity" you have to go further out by a distance that effectively lowers the value of g (Sun) at least twenty five times.

Now, we know (from the formula for g) that the g-value decreases as the SQUARE of the distance from the Sun.

Thus, taking the square root of 25 we get 5.

This must be the factor increase on R to get the value of g down to at least 1.1 time Earth's. Check this out:

take 5 x R =  5 x (6.96 x 10^8 m) =  3.48 x 10^9 m

obtain the new value from the original formula (GM remains constant only the distance changes):

g =   GM /  3.48 x 10^9   =  10.96 m/s^2

which is about 1.1 the Earth value.

Further adjustment will disclose that you will get about 0.9 the Earth value by increasing the distance from the Sun's surface to R' = 3.9 x 10^9 m.

You can easily see this is *outside* the corona, since the corona's scale height is approx. 50,000 km or 5 x 10 ^7 m and the nearest of your "g-thresholds" (for 1.1. times g) is at least 2.78 x 10^9 m (e.g. R' - R) above the photosphere, or four times the solar radius *beyond the photosphere*.

The different parts of the solar interior and the solar atmosphere structure can be found at the link below, which includes a niece graphic as well:

http://solar.physics.montana.edu/YPOP/Spotlight/SunInfo/Structure.html