Question

Сила гравитационного притяжения космонавта на поверхности Земли равно 800H.Чему будет равна сила гравитационного притяжения этого космонавта на поверхности планеты, масса которой в 80 раз меньше массы Земли и радиус которой в 4 раза меньше радиус Земли?

Answer 1

P=800 H ; m=800/10 кг = 80 кг
M0=80M; R0=4R
$F=G \frac{mM}{ R^{2} } = G \frac{80*M0*16}{80*R0^{2} } =16g=160H$

Answer 2

Calculation of Gravitational Force

To calculate the gravitational force between two objects, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Let's denote the mass of the astronaut as m1, the mass of the planet as m2, the radius of the Earth as r1, and the radius of the other planet as r2.

According to the information given, the gravitational force on the surface of the Earth acting on the astronaut is 800H. We need to find the gravitational force on the surface of the other planet acting on the same astronaut.

Using Newton's law of universal gravitation, we can set up the following equation:

F1 = G * (m1 * m2) / r1^2

where F1 is the gravitational force on the surface of the Earth, G is the gravitational constant, m1 is the mass of the astronaut, m2 is the mass of the Earth, and r1 is the radius of the Earth.

We also know that the mass of the other planet is 80 times smaller than the mass of the Earth, and the radius of the other planet is 4 times smaller than the radius of the Earth.

Let's denote the gravitational force on the surface of the other planet as F2.

Using the same equation, we can write:

F2 = G * (m1 * (m2/80)) / (r2/4)^2

To find the value of F2, we need to substitute the known values into the equation and solve for F2.

Calculation

Substituting the values into the equation, we get:

800H = G * (m1 * m2) / r1^2

F2 = G * (m1 * (m2/80)) / (r2/4)^2

Since we are only interested in the ratio of the gravitational forces, we can divide the second equation by the first equation:

F2 / 800H = (G * (m1 * (m2/80)) / (r2/4)^2) / (G * (m1 * m2) / r1^2)

Simplifying the equation, we get:

F2 / 800H = ((m2/80) / (r2/4)^2) / (m2 / r1^2)

Cancelling out the common factors, we have:

F2 / 800H = (1/80) * (r1^2 / (r2/4)^2)

Simplifying further, we get:

F2 / 800H = (1/80) * (r1^2 / (r2^2 / 16))

F2 / 800H = (1/80) * (16 * r1^2 / r2^2)

F2 / 800H = (1/5) * (r1^2 / r2^2)

Finally, we can solve for F2:

F2 = (1/5) * (r1^2 / r2^2) * 800H

Calculation Result

Using the given values, we can substitute them into the equation to find the value of F2:

F2 = (1/5) * (r1^2 / r2^2) * 800H

Substituting the values:

F2 = (1/5) * ((r1/4)^2 / r2^2) * 800H

Now, we can calculate the value of F2.