A space vehicle is traveling at 4450 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 64 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (km/h) of the command module relative to Earth after the separation?

Hunting a black hole. Observations of the light from a certain star indicate that it is part of a binary (two-star) system. This visible star has moves in a circle of radius r1 and has orbital period T. Variations in the brightness of nearby stars suggest that the unseen companion moves in a circle of radius r2 (see the figure). Find the approximate masses (a) m1 of the visible star and (b) m2 of the dark star. Express your answer in terms of r1, r2, T, and G. I asked this question before and recieved an incorrect answer, so I'm asking again.

After the NEAR spacecraft passed Mathilde, on several occasions rocket propellant was expelled to adjust the spacecraft's momentum in order to follow a path that would approach the asteroid Eros, the final destination for the mission. After getting close to Eros, further small adjustments made the momentum just right to give a circular orbit of radius 45 km (45 × 103 m) around the asteroid. So much propellant had been used that the final mass of the spacecraft while in circular orbit around Eros was only 550 kg. The spacecraft took 1.04 days to make one complete circular orbit around Eros. Calculate what the mass of Eros must be.

Answer without rounding off: Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 3.9 x 106 m through the center of a planet with a radius of 8.8 x 106 m. If the mass of the planet is 42.2 x 1015 kg, measure the displacement of the ball at time t = 6 s?

(Gauss's Law for Mass) Journey through the Center of the Earth. A 1024-kg blue ball is dropped from an initial z-position of 3.8 x 106 m through the center of a planet with radius 8.5 x 106 m. If the mass of the planet is 48.8 x 1015 kg, measure the displacement of the ball at time t = 7 s

The proton is traveling at a constant speed of 5.5 × 105 m/s, and the radius of the kissing circle is 0.02 m. The mass of a proton is 1.7 × 10-27 kg. When the proton is at location A, what are the magnitude and direction (d|p→|/d⁢t)(p^) of the parallel component of dp→/d⁢t?

A binary star consist of two stars of the same mass m revolving in a circle of radius R about their common centre of mass. Suppose that a meteorite passes through the centre of mass of the binary star in a direction perpendicular to the orbital plane. What is the minimum speed that the meteorite must have at the centre of mass in order for it to escape from the gravitational attraction of the binary star? ANSW: 4Gm R w

In the figure below, a square of edge length s is formed by four spheres of masses, m1, m2, m3, and m4. What is the x component and the y component of the net gravitational force from them on a central sphere of mass m5. State your answers in terms of the given variables. ( Use any variable or symbol stated above along with the following as necessary: and G for the gravitational constant.)

A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet.  a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.

A small astronomical object falls toward the Mars. It starts from rest with respect to the Mars when it is at the height 5220 km above the Mars’ surface. With what speed will the object strike the Mars's surface? The Mars' radius and mass are 3390 km and 6.39*1023 kg, respectively.