Pluto has a mass of 1.30 1022 kg and a radius of 1.18 106 m

(a) What is the acceleration due to gravity on Pluto?
(b) How much would a 4.7-kg person weigh on this planet?

a) GMp/r^2

b) GMp*4.7/r^2

To find the acceleration due to gravity on Pluto, you can use the formula:

acceleration due to gravity (g) = (gravitational constant * mass of Pluto) / (radius of Pluto)^2

(a) The gravitational constant is a constant value represented by G = 6.67430 x 10^-11 N(m/kg)^2.

Plugging in the values for mass and radius of Pluto:

g = (6.67430 x 10^-11 N(m/kg)^2 * 1.30 x 10^22 kg) / (1.18 x 10^6 m)^2

Simplifying the equation:
g = (6.67430 x 10^-11 N(m/kg)^2 * 1.30 x 10^22 kg) / (1.39 x 10^12 m^2)

Calculating the acceleration due to gravity on Pluto:
g ≈ 0.6206 m/s^2

Therefore, the acceleration due to gravity on Pluto is approximately 0.6206 m/s^2.

(b) To determine how much a 4.7-kg person would weigh on Pluto, you can use the formula:

Weight (W) = mass (m) * acceleration due to gravity (g)

Plugging in the values:

W = 4.7 kg * 0.6206 m/s^2

Calculating the weight of the person on Pluto:
W ≈ 2.9182 N

Therefore, a 4.7-kg person would weigh approximately 2.9182 Newtons on Pluto.

To find the acceleration due to gravity and the weight of a person on Pluto, we can use the following formulas:

(a) The acceleration due to gravity (g) can be calculated using the formula:

g = G * (M / r^2)

where:
G is the universal gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M is the mass of Pluto (1.30 × 10^22 kg)
r is the radius of Pluto (1.18 × 10^6 m)

(b) The weight of a person can be calculated using the formula:

Weight = mass * g

where:
mass is the mass of the person (4.7 kg)
g is the acceleration due to gravity on Pluto (from part a)

Let's calculate these step-by-step:

(a) Calculating the acceleration due to gravity on Pluto:

Step 1: Substitute the given values into the formula:

g = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.30 × 10^22 kg) / (1.18 × 10^6 m)^2

Step 2: Simplify the equation inside the brackets:

g = (6.67430 × 1.30 × 10^22 kg * 10^-11 m^3 kg^-1 s^-2) / (1.18 × 10^6 m)^2

Step 3: Solve the equation:

g = (8.674790000000001 × 10^11 m^3 kg^-1 s^-2) / (1.3924 × 10^12 m^2)

Step 4: Simplify the units and divide:

g = 6.218 m/s^2

(b) Calculating the weight of a 4.7-kg person on Pluto:

Step 5: Substitute the mass of the person and the acceleration due to gravity into the formula:

Weight = 4.7 kg * 6.218 m/s^2

Step 6: Calculate the weight:

Weight = 29.1826 N

Therefore,

(a) The acceleration due to gravity on Pluto is approximately 6.218 m/s^2.
(b) A 4.7-kg person would weigh approximately 29.1826 Newtons on Pluto.