Calculating the Velocity of Escape from the Sun

To calculate the velocity of escape from the Sun, we need to consider the mass of the Sun and its distance from Earth.

Given:
- Mass of the Sun (m) = 1.89 × 10^30 kg
- Distance from Earth to the Sun (d) = 1.59 × 10^8 km

Formula:
The velocity of escape (V) can be calculated using the formula:

V = √(2GM/r)

Where:
- G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the Sun
- r is the distance from Earth to the Sun

Converting Units:
Before applying the formula, we need to convert the given values to appropriate units.

- Convert the distance from km to meters:
1.59 × 10^8 km = 1.59 × 10^11 m

- Convert the mass of the Sun from kg to g:
1.89 × 10^30 kg = 1.89 × 10^33 g

Calculating the Velocity of Escape:
Now, we can substitute the values into the formula to calculate the velocity of escape.

V = √(2 * 6.67430 × 10^-11 * 1.89 × 10^33 / 1.59 × 10^11)

Simplifying the equation further:

V = √(2 * 6.67430 × 1.89 / 1.59) × √(10^33 / 10^11)

V = √(2 * 6.67430 × 1.89 / 1.59) × √(10^(33-11))

V = √(2 * 6.67430 × 1.89 / 1.59) × √(10^22)

V = √(2 * 6.67430 × 1.89 / 1.59) × 10^11

V = 2.242 × 10^5 m/s

Conclusion:
Therefore, the velocity of escape from the Sun is approximately 2.242 × 10^5 m/s.