An astronaut of mass 80 kg lands on a planet,the radius of which is half that of the earth and the mass of which is three times that of earth.what will be the force of attraction which this planet has on him?
F = G M m /(r^2) = m g
= G M (3m)/(.25 r^2) = 12 G M m/r^2
so 12 m g = 12 * 80 * 9.81
= 9418 Newtons
To find the force of attraction between the astronaut and the planet, we can use Newton's law of universal gravitation, which states that the force of attraction between two objects is given by the equation:
F = (G * m1 * m2) / r^2
Where:
F is the force of attraction
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
In this case, the mass of the astronaut (m1) is given as 80 kg. The mass of the planet (m2) is three times the mass of the Earth, so it will be 3 * (mass of Earth).
The radius of the planet is given as half the radius of Earth, which means it will be half the distance between the centers of the two objects.
Let's plug in the values and calculate the force:
m1 = 80 kg
m2 = 3 * (mass of Earth)
r = (radius of Earth) / 2
Now, we need to find the mass of the Earth. The mass of the Earth is approximately 5.972 × 10^24 kg.
m2 = 3 * (5.972 × 10^24 kg)
Next, we need to find the radius of the Earth. The average radius of the Earth is approximately 6,371 km.
r = 6,371 km / 2
Now, we can plug in the values and calculate the force:
F = (6.67430 × 10^-11 N m^2/kg^2) * (80 kg) * [3 * (5.972 × 10^24 kg)] / [(6,371 km / 2)^2]
After evaluating this equation, you will get the force of attraction between the astronaut and the planet.