A projectile is shot directly away from Earth's surface. Neglect the rotation of the Earth. What multiple of Earth's radius RE gives the radial distance (from the Earth's center) the projectile reaches if (a) its initial speed is 0.562 of the escape speed from Earth and (b) its initial kinetic energy is 0.562 of the kinetic energy required to escape Earth? (Give your answers as unitless numbers.) (c) What is the least initial mechanical energy required at launch if the projectile is to escape Earth? (a) Number Units Units (b) Number Units (c) Number

Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.

Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 5390 km. Satellite B is to orbit at an altitude of 22500 km. The radius of Earth REis 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit? (b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit? (c) Which satellite (answer A or B) has the greater total energy if each has a mass of 11.7 kg? (d) By how much?

A satellite orbits a planet of unknown mass in a circle of radius 2 × 107 m. The magnitude of the gravitational force on the satellite from the planet is F = 80 N. a) What is the kinetic energy of the satellite in this orbit? b) What would F be if the orbit radius were increased to 3 x 107 m?

(a) Calculate the work (in MJ) necessary to bring a 105 kg object to a height of 1004 km above the surface of the Earth. MJ (b) Calculate the extra work (in J) needed to launch the object into circular orbit at this height.

Macmillan Learning A planet is in an elliptical orbit around a distant star. At periastron (the point of closest approach to the star), the planet is rp = 3.90 × 108 km from the star and is moving with a speed of Up = 21.5 km/s. When the planet is at apastron (the point of greatest distance from the star), it is ra = 9.00 × 108 km from the star. "P Va = HH How fast is the planet moving at apastron? V km/s

Two concentric spherical shells with uniformly distributed masses M₁ and M₂ are situated as shown in the figure. Find the magnitude of the net gravitational force on a particle of mass m, due to the shells, when the particle is located at each of the radial distances shown in the figure. Fa NOTE: Give your answer in terms of the variables given and G when applicable (a) What is the magnitude of the net gravitational force if the particle is located outside both shells with a radial distance a? F = M₁ (b) What is the magnitude of the net gravitational force if the particle is located between the two shells with a radial distance b? Fc M₂ ****** - a (c) What is the magnitude of the net gravitational force if the particle is located inside both shells with a radial distance c? =

Physics A white dwarf is the remnant core of a previous star < 8 solar masses that has about the mass of the Sun but the radius of the Earth. What would be (1) the orbital speed and (2) the orbital period for a spacecraft in orbit just above the surface of the white dwarf?