A planet with a mass of 5.67E25 kg has a radius of 3.63E7 m. How much would a 89 kg person weigh on this planet if they were standing on the surface?
To find the weight of a person on a different planet, we need to use the gravitational force equation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (6.67 x 10^-11 N*m^2/kg^2)
m1 and m2 are the masses of the two objects experiencing the gravitational force
r^2 is the distance between the centers of the two objects squared
In this case, the weight of the person is equivalent to the gravitational force between the person and the planet.
To calculate the weight of the person, we need to determine the mass of the planet (m1), the mass of the person (m2), and the distance between them (radius of the planet, r).
Given:
Mass of the planet (m1) = 5.67 x 10^25 kg
Mass of the person (m2) = 89 kg
Radius of the planet (r) = 3.63 x 10^7 m
Let's plug in these values into the formula:
F = (6.67 x 10^-11 N*m^2/kg^2) * ((5.67 x 10^25 kg) * (89 kg)) / (3.63 x 10^7 m)^2
To simplify the calculation, we can first calculate the denominator:
(3.63 x 10^7 m)^2 = (3.63 x 10^7 m) * (3.63 x 10^7 m) = 1.32169 x 10^15 m^2
Now, substitute the values into the formula:
F = (6.67 x 10^-11 N*m^2/kg^2) * ((5.67 x 10^25 kg) * (89 kg)) / (1.32169 x 10^15 m^2)
Multiplying the masses:
(5.67 x 10^25 kg) * (89 kg) = 5.05163 x 10^27 kg^2
Substituting the above result:
F = (6.67 x 10^-11 N*m^2/kg^2) * (5.05163 x 10^27 kg^2) / (1.32169 x 10^15 m^2)
Now, multiply (6.67 x 10^-11 N*m^2/kg^2) with (5.05163 x 10^27 kg^2):
(6.67 x 10^-11 N*m^2/kg^2) * (5.05163 x 10^27 kg^2) = 3.36864 x 10^17 N
Finally, divide by (1.32169 x 10^15 m^2):
F = 3.36864 x 10^17 N / (1.32169 x 10^15 m^2)
F ≈ 254.929 N (rounded to three decimal places)
Therefore, a person weighing 89 kg on Earth would weigh approximately 254.929 N on a planet with the given mass and radius.