Question

////////////СРОЧНО|||||||||||||||||||||||УМОЛЯЮ,ДАМ ЛУЧШИЙ ОТВЕТ Супутник рухається по коловій орбіті навколо деякої планети на висоті, що дорівнює радіусу цієї планети. Прискорення руху супутника 0,95м/с2. Визначте масу планети та період обертання супутника. Радіус планети дорівнює 3400 км.

Answer 1

Calculation of the Planet's Mass:

To determine the mass of the planet, we can use the formula for the centripetal acceleration of an object moving in a circular orbit:

a = v^2 / r

Where: - a is the centripetal acceleration - v is the orbital velocity of the satellite - r is the radius of the orbit

In this case, we are given the centripetal acceleration (a) as 0.95 m/s^2 and the radius of the planet (r) as 3400 km (which is equivalent to 3,400,000 meters). We need to find the orbital velocity (v).

To find the orbital velocity, we can use the formula for the gravitational force acting on the satellite:

F = G * (m1 * m2) / r^2

Where: - F is the gravitational force - G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2) - m1 is the mass of the planet - m2 is the mass of the satellite - r is the radius of the orbit

The gravitational force can also be expressed as:

F = m2 * a

Since the mass of the satellite is much smaller than the mass of the planet, we can assume that m2 is negligible compared to m1. Therefore, we can rewrite the equation as:

m1 * a = G * m1 * m2 / r^2

Simplifying the equation, we find:

a = G * m1 / r^2

Solving for m1, we get:

m1 = a * r^2 / G

Let's calculate the mass of the planet using the given values:

a = 0.95 m/s^2 r = 3,400,000 meters G = 6.67430 × 10^-11 m^3 kg^-1 s^-2

Substituting these values into the equation, we can find the mass of the planet.