A planet has a mass of 6.06x 10^23 kg and a radius of 3.99 x 10^6 m. a) What is the acceleration due to gravity on this planet? b) how much would a 72.5 kg person weigh on this plane?
"g"= GMp/radius^2
weight= 72.5*"g"
m g = G m M/r^2
so
g = G M/r^2 = 6.67*10^-11 * 6.06*10^23 *10^-12 / 3.99^2
= 40.42 * 10^0
= 40.42 or about 4 times earth g
m g = 72.5*40.42 = 2930 Newtons
To find the acceleration due to gravity on the planet, you can use the equation:
a = (G * M) / R^2
where:
- a represents the acceleration due to gravity
- G is the universal gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the planet
- R is the radius of the planet
Now let's calculate the values step by step:
a) Calculation of acceleration due to gravity:
- G = 6.67430 × 10^-11 m^3 kg^-1 s^-2
- M = 6.06 × 10^23 kg
- R = 3.99 × 10^6 m
Substituting these values into the equation, we get:
a = (6.67430 × 10^-11 * 6.06 × 10^23) / (3.99 × 10^6)^2
Now we can calculate the acceleration due to gravity on this planet.
b) To calculate how much a person would weigh on this planet, we can use the formula:
Weight = mass * acceleration due to gravity
Given:
- mass of the person = 72.5 kg
- acceleration due to gravity on this planet (from part a)
Substituting the values into the equation, we can calculate the weight of the person on this planet.