A planet has a mass of 6.22 × 1023 kg and a radius of 2.51 × 106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 77.7-kg person weigh on this planet?
W = m•g =G•m•M/R²
g= G•M/R²
the gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
Earth’s mass is M = 5.97•10²⁴kg,
Earth’s radius is R = 6.378•10⁶ m.
To find the acceleration due to gravity on a planet, we can use the formula for gravitational acceleration:
(a) To find the acceleration due to gravity on the planet, we 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 N(m/kg)^2)
- M is the mass of the planet
- r is the radius of the planet
Plugging in the values given in the question:
M = 6.22 × 10^23 kg
r = 2.51 × 10^6 m
We get:
g = (6.67 × 10^-11 N(m/kg)^2 * 6.22 × 10^23 kg) / (2.51 × 10^6 m)^2
Calculating this expression will give us the acceleration due to gravity on the planet.
(b) To find out how much a 77.7-kg person would weigh on the planet, we can use the formula for weight:
Weight = mass * g
where:
- Weight is the force experienced by the person (measured in newtons, N)
- mass is the mass of the person
- g is the acceleration due to gravity
Using the value of the acceleration due to gravity we calculated in part (a), we can substitute it and the given mass value into the formula to find the weight.
So let's calculate both parts:
(a) Plugging the values into the formula, we get:
g = (6.67 × 10^-11 N(m/kg)^2 * 6.22 × 10^23 kg) / (2.51 × 10^6 m)^2
Simplifying and calculating the expression will give us the value of g, the acceleration due to gravity on the planet.
(b) Using the value of g from part (a) and the given mass of the person (77.7 kg), we can calculate the weight:
Weight = 77.7 kg * g
Calculating this expression will give us the weight of the person on the planet.