A satellite with mass 6.00*10^3 is in the equatorial plane in a circular orbit. The planet's mass = 6.59 *10^25 and a day of length is 1.6 earth days. How far from the center (in m) of the planet is the satellite? What is the escape velocity (km?sec) from the orbit?
please tell the main formula
To find the distance from the center of the planet to the satellite in meters, we can use the formula for the centripetal force:
F = (G * m1 * m2) / r^2
where F is the gravitational force between the planet and the satellite, G is the gravitational constant (6.67430 × 10^-11 m^3 / kg / s^2), m1 is the mass of the planet, m2 is the mass of the satellite, and r is the distance from the center of the planet to the satellite.
In a circular orbit, the force of gravity provides the necessary centripetal force to keep the satellite in orbit. So we can equate the two:
F = (G * m1 * m2) / r^2 = m2 * v^2 / r
Where v is the orbital speed of the satellite. Rearranging the equation, we get:
v^2 = (G * m1) / r
We can solve this equation to find the value of v (orbital speed of the satellite). Then, we can use this to calculate the radius (r).
To find the escape velocity, we use the formula:
v_escape = sqrt(2 * G * m1 / r)
Where v_escape is the escape velocity, G is the gravitational constant, m1 is the mass of the planet, and r is the distance from the center of the planet to the satellite.
Using these formulas, we can calculate the values for the distance from the center of the planet to the satellite and the escape velocity.