A planet has a mass of 5.21x10^23 kg and a radius of 2.77x10^6 m. (a) what is the acceleration of this planet? (b) how much would a 65kg person weigh on this planet?
On earth, g = 9.81 m/s^2 because GM/r^2 = 9.81
So, for your planet, plug in those values and crank out the value of g', the new gravitational acceleration.
Then, for (b), F = mg'
To find the acceleration of the planet, you can use Newton's law of universal gravitation. The formula for calculating the acceleration due to gravity is given as:
a = (G * M) / r^2
where a is the acceleration, G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2), M is the mass of the planet, and r is the radius of the planet.
a) Substituting the given values into the equation:
M = 5.21 × 10^23 kg
r = 2.77 × 10^6 m
G = 6.67430 × 10^-11 N m^2/kg^2
a = (6.67430 × 10^-11 N m^2/kg^2 * 5.21 × 10^23 kg) / (2.77 × 10^6 m)^2
Simplifying the expression gives:
a ≈ 9.71 m/s^2
Therefore, the acceleration of the planet is approximately 9.71 m/s^2.
b) To determine how much a 65 kg person would weigh on this planet, we can use Newton's law of gravity:
F = (G * m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, the person and the planet), and r is the distance between their centers (the planet's radius in this case).
In this scenario, m1 is the mass of the person (65 kg), m2 is the mass of the planet (5.21 × 10^23 kg), and r is the radius of the planet (2.77 × 10^6 m).
F = (6.67430 × 10^-11 N m^2/kg^2 * 65 kg * 5.21 × 10^23 kg) / (2.77 × 10^6 m)^2
Simplifying the expression gives:
F ≈ 2.094 N
Therefore, a 65 kg person would weigh approximately 2.094 Newtons on this planet.
(a) g = G * mass / radius = 6.67E-11 * 5.21E23 / 2.77E6 ... m/s^2
(b) 65 * g = ? ... N