A planet has a mass of 6.08 × 1023 kg and a radius of 2.62 × 106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 63.6-kg person weigh on this planet?
To find the acceleration due to gravity on a planet, we can use the formula:
g = G * (M / R^2),
where g is the acceleration due to gravity, G is the gravitational constant (approximately 6.67 × 10^-11 Nm^2/kg^2), M is the mass of the planet, and R is the radius of the planet.
(a) Acceleration due to gravity on the planet:
Plug in the values into the formula:
g = 6.67 × 10^-11 Nm^2/kg^2 * (6.08 × 10^23 kg / (2.62 × 10^6 m)^2)
Simplify the equation:
g = 6.67 × 10^-11 Nm^2/kg^2 * (6.08 × 10^23 kg / 6.858 × 10^12 m^2)
g = (4.84736 × 10^13 N) / (6.858 × 10^12 m^2)
Divide the numerator by the denominator:
g ≈ 7.07 m/s^2
Therefore, the acceleration due to gravity on this planet is approximately 7.07 m/s^2.
(b) Weight of a 63.6-kg person on this planet:
To find the weight of a person, we can use the formula:
Weight = mass * acceleration due to gravity.
Using the value of the person's mass (63.6 kg) and the acceleration due to gravity on the planet (7.07 m/s^2), we can calculate the weight:
Weight = 63.6 kg * 7.07 m/s^2
Weight ≈ 449.55 N
Therefore, a 63.6 kg person would weigh approximately 449.55 Newtons on this planet.