Gravity in equator versus pole of Sun

GRAVITY IN EQUATOR V/S POLE OF SUN

The Sun is the star at the center of our Solar System. Gravity on the surface of Sun varies due to its rotation. Since Sun rotates, all points on its surface perform circular motion except the North and South Pole. The points at equator perform circular motion of maximum radii as compared to other points. The polar points do not perform circular motion but rotate about their own axis. 

Consider two points, equator and North Pole on Sun’s surface. We’ll compare acceleration due to gravity (g) between these two points.

 

ASSUMPTIONS

• The equator and pole locations are not terrain but plains

• Density of Sun is constant throughout

• Sun is a perfect homogeneous sphere

• Angular velocity is constant throughout

• Effect of gravity of satellites [planets] is negligible

PHYSICAL CHARACTERISTICS

Mean Radius R= 695,700 km

Mass M = 2*10³⁰ kg

Rotational Time period T = 25.38 days

CALCULATION

Acceleration due to gravity on pole:

g = GM/R²

G – Universal Gravitation constant = 6.67*10^-11 Nm²/kg²

g = [6.67*10^-11 * 2*10³⁰]/ [695700*1000]²

g = 275.6206 m/s²

g (φ) = 275.62 m/s²

φ – Latitude = 90⁰ for poles

Average Angular velocity:

ω = 2π / T (rad/s)

ω = 2π / [25.38*86,400] (rad/s) 

ω = 2π/2,192,832

ω = 2.863876*10^-6 rad/s

Acceleration due to gravity on equator:

We can find acceleration due to gravity on equator by using the formula,

g’(φ) = g(φ) – Rω²cos²φ

φ - Latitude = 0⁰ for equator

g’(φ) = 275.62 – 695,700,000*(2.863876*10^-6)²

g’(φ) = 275.62 – 5.7059*10^-3

g’(φ) = 275.6142 m/s²

CONCLUSION

On comparing g (φ) and g’ (φ) we observe that gravity at pole is just slightly greater than that at the equator. This is because the Sun rotates so slow that it cannot produce enough angular velocity at the equator to reduce the acceleration due to gravity.

The difference is g (φ) - g’ (φ) = 275.62 – 275.6142 = 5.7059*10^-3 m/s²

For a body of mass 50Kg,

Weight at pole = 50* g (φ) = 50*275.62 = 13,781 N

Weight at equator = 50* g’ (φ) = 50*275.6142 = 13,780.7 N

Thus a body will weigh approximately 0.3 N more in pole than equator.