Understanding the Concepts
* Surface Gravity: The acceleration due to gravity at the surface of an object.
* Newton's Law of Universal Gravitation: F = G * (m1 * m2) / r², where:
* F is the force of gravity
* G is the gravitational constant (6.674 x 10⁻¹¹ N m²/kg²)
* m1 and m2 are the masses of the two objects
* r is the distance between their centers
* Acceleration due to Gravity: g = F/m, where:
* g is the acceleration due to gravity
* F is the force of gravity
* m is the mass of the object experiencing the force
Calculations
1. Mass of the White Dwarf (m1): Assume the mass of the white dwarf is equal to the mass of our Sun (M☉ = 1.989 x 10³⁰ kg).
2. Radius of the White Dwarf (r): We're told it's the size of our Moon, so its radius is approximately 1,737 km (1.737 x 10⁶ m).
3. Calculate the Surface Gravity (g):
* Substitute the values into the acceleration due to gravity formula:
g = (G * m1) / r²
g = (6.674 x 10⁻¹¹ N m²/kg² * 1.989 x 10³⁰ kg) / (1.737 x 10⁶ m)²
g ≈ 4.37 x 10⁶ m/s²
Result:
The surface gravity of a white dwarf star with the mass of our Sun and the size of our Moon is approximately 4.37 x 10⁶ m/s². This is about 445,000 times stronger than the surface gravity of Earth!
Important Note: This is a simplified calculation. White dwarf stars have complex internal structures and their surface gravity can vary slightly depending on their specific composition and internal pressure.
