There is a satellite of mass m in an orbit radius R about a planet with...

There is a satellite of mass m in an orbit radius R about a planet with mass M.

a. What is the sum of the kinetic energy and the gravitational potential energy of the satellite?

b. What is the energy required for the satellite to escape the planet's gravity?

Expert Solution

genius_generous answered 2 months ago

A satellite with Mass m is in orbit with a constant radius around the earth r0...

A satellite with Mass m is in orbit with a constant radius around the earth r0 (RE=6370km, Mass ME = 5,98*1024kg) a) Show that the satellite moves with uniform circular motion and calculate the velocity v0 in dependance of G,M E and R E . b) At which height h above the earth's surface is the geostationary orbit found? Which linear velocity does a satellite have at this height? c) Compare this to the linear velocity on earth's surface as...

1.Consider a satellite of the earth in a circular orbit of radius R. Let M and...

1.Consider a satellite of the earth in a circular orbit of radius R. Let M and m be the mass of the earth and that of the satellite, respectively. Show that the centripetal acceleration of the satellite is aR = -(v^2/R)*(r/r) where v = |v| is the magnitude of the velocity V and r/r is a unit vector in the radial direction. 2.Using Newton's second low of motion and the law of universal gravitation, determine the speed v=|V| and the...

A satellite of mass 100 kg is in circular orbit about planet Uzaz, which has a...

A satellite of mass 100 kg is in circular orbit about planet Uzaz, which has a mass M and radius R, at an altitude (above the surface) h. (a) (2 points) Express the linear speed v of the satellite in terms of the given variables and the universal gravitational constant. (b) (3 points) Suppose that if h = 1 × 104 km, the period of the orbit is T = 11 hours. If Uzaz has a mass of 7.0 ×...

Assume a planet with mass M and radius R. (a) Find the strength of its gravitational...

Assume a planet with mass M and radius R. (a) Find the strength of its gravitational field at the surface, g. [5] (b) Find the escape velocity, vesc, for a mass on the planet's surface in terms of M and R. [10] (c) Show that vesc=√2gR . [3] (d) Calculate the numeric value of the escape velocity from Earth without using Earth's mass. [2]

A planet of mass 6 × 1025 kg is in a circular orbit of radius 4...

A planet of mass 6 × 1025 kg is in a circular orbit of radius 4 × 1011 m around a star. The star exerts a force on the planet of constant magnitude 1.8 × 1023 N. The speed of the planet is 3.4 × 104 m/s. (a) In half a "year" the planet goes half way around the star. What is the distance that the planet travels along the semicircle? (b) During this half "year", how much work is...

1. A certain satellite travels in an approximately circular orbit of radius 7.5 × 106 m...

1. A certain satellite travels in an approximately circular orbit of radius 7.5 × 106 m with a period of 6 h 27 min. Calculate the mass of its planet from this information 2. (a) At what height above Earth's surface is the energy required to lift a satellite to that height equal to the kinetic energy required for the satellite to be in orbit at that height? (b) For greater heights, which is greater, the energy for lifting or...

A spaceship of mass ? is on a circular orbit around a planet of mass ?,...

A spaceship of mass ? is on a circular orbit around a planet of mass ?, and is moving with constant speed ?0. (a) What is the radius of the orbit of the spaceship? A sudden explosion tears the spaceship into two pieces of equal mass. Piece 1 leaves the explosion with speed 4?0/5 with its velocity is in the same direction of the velocity of the spaceship before the explosion. As ? ≪ ?, the gravitational attraction between the...

The moment of inertia of a thin ring of mass M and radius R about its...

The moment of inertia of a thin ring of mass M and radius R about its symmetry axis is ICM = MR2 Kira is working the ring-toss booth at a local carnival. While waiting for customers, Kira occupies her time by twirling one of the plastic rings of mass M and radius R about her finger. Model the motion of the plastic ring as a thin ring rotating about a point on its circumference. What is the moment of inertia of...

A spherical satellite of radius 4.8 m and mass M = 210 kg is originally moving...

A spherical satellite of radius 4.8 m and mass M = 210 kg is originally moving with velocity satellite,i = < 2800, 0, 0 > m/s, and is originally rotating with an angular speed ω1 = 2 radians/second, in the direction shown in the diagram. A small piece of space junk of mass m = 3.9 kg is initially moving toward the satellite with velocity junk,i = < -2600, 0, 0 > m/s. The space junk hits the edge of...

a uniform spherical shell of mass M and radius R rotates about a vertical axis on...

a uniform spherical shell of mass M and radius R rotates about a vertical axis on frictionless bearing. A massless cord passes around the equator of the shell, over a pulley of rotational inertia I and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h from rest?...

Question