the sun's mass is 1.99*10^30 kg and it has a radius of 6.96*10^8 m.What is the Sun's gravitational field strength at its surface.
To calculate the gravitational field strength at the surface of the Sun, you can use the formula:
g = G * (mass of the Sun) / (radius of the Sun)^2
Where:
- g is the gravitational field strength
- G is the gravitational constant (approximately 6.67 * 10^-11 N*m^2/kg^2)
- The mass of the Sun is given as 1.99 * 10^30 kg
- The radius of the Sun is given as 6.96 * 10^8 m
Plugging in the values, we can calculate the gravitational field strength:
g = (6.67 * 10^-11 N*m^2/kg^2) * (1.99 * 10^30 kg) / (6.96 * 10^8 m)^2
To simplify the calculation, let's break it down into steps:
Step 1: Calculate the numerator
Numerator = (6.67 * 10^-11 N*m^2/kg^2) * (1.99 * 10^30 kg)
= 13.2333 * 10^19 N*m
Step 2: Calculate the denominator
Denominator = (6.96 * 10^8 m)^2
= 48.4416 * 10^16 m^2
Step 3: Divide the numerator by the denominator
Gravitational field strength (g) = Numerator / Denominator
= 13.2333 * 10^19 N*m / 48.4416 * 10^16 m^2
To divide these quantities with exponents, subtract the exponents:
Gravitational field strength (g) = 2.7301282 * 10^3 N/kg
Therefore, the Sun's gravitational field strength at its surface is approximately 2.73 * 10^3 N/kg.