Sirius is the brightest star in the night sky. It has a radius of 2.5 x 10^9 m and a mass of 5.0 x 10^31 kg. Determine the following...

Question

Sirius is the brightest star in the night sky. It has a radius of 2.5 x 10^9 m and a mass of 5.0 x 10^31 kg. What is the gravitational force on a 1.0 kg mass as its surface?

Please include a detailed and understandable answer for a Grade 11. Thanks :)

Answer 1

The force, that acts on the unit mass on the surface of a star or planet, we call gravitational field strength or acceleration of free fall g. The formula for it is well known:

g = G M / R²

Putting the values for universal gravitational constant, mass and radius of Sirius, we obtain

g = 6.67 x 10 ^{- 11} Nm²/kg² · 5.0 x 10 ³¹ kg / (2.5 x 10 ⁹ kg)² = 5.3 x 10 ² N/kg

BTW, it is easy to show that the unit of g could be also m / s² .

Answer 2

The gravitational force can be calculated using the following equation:

F = GMm/R²

Where G = 6.67 x 10^-11 (universal gravitational constant)

m is the mass of the object = 1 kg

M is the mass of the star = 5 x 10³¹ kg

R is the radius between the object and the center of the star, which is simply the radius = 2.5 x 10⁹ m

Now we can plug in these values.

F = (6.67 x 10^-11) (5 x 10³¹) (1) / (2.5 x 10⁹)²

F = 5.336 x 10² N