A spaceship approaches the Moon (mass `= M` and radius `= R` along a parabolic path which is almost tangential to its surface. At the moment of the maximum approach, the brake rocket is fired to convert the spaceship into a satellite of the Moon. Find the change in speed.

A spaceship approaches the Moon along a parabolic trajectory which is almost tangent to the Moon's surface. At the moment of the maximum approach the brake rocket was fired for a short time interval, and the spaceship was transferred into a circular orbit of a Moon satellic. Find how the spaceship velocity modulus increased in the process of braking.

A ball of mass m and radius r rolls along a circular path of radius R its speed at the bottom (theta=0^(@)) of the path is v_(0) find the force of the path on the ball as a function of theta .

A small asteroid is approaching a planet of mass M and radius R from a large distance. Initially its velocity (u) is along a tangent to the surface of the planet. It fall on the surface making an angle of 30^(2) with the vertical. Calculate u.

The moment of inertia of a disc of mass M and radius R about an axis. Which is tangential to sircumference of disc and parallel to its diameter is.

A hoop with mass M and radius R lies flat on a perfectly smooth surface. An insect with mass m rests on it. On being distrubed by some noise it starts crawling on the hoop with speed v. Find the trajectory of the centre of the hoop and its speed.

A spaceship is sent to investigate a planet of mass M and radius R . While hanging motionless in space at a distance 5R from the centre of the planet, the spaceship fires an instrument package of mass m , which is much smaller than the mass of the spaceship. For what angle theta will the package just graze the surface of the planet?

A satellite of mass m revolves around the earth of radius R at a hight x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

Spacemen Fred's spaceship (which has negligible mass) is in an elliptical orbit about planet Bob. The minimum distance between the spaceship and the planet is R, the maximum distance between the spaceship and the planet is 2R. At the point of maximum distance, spaceman fred is traveling at speed v_(0) . he then fires his thrusters so that he enters a circular orbit of radius 2R. what is his new speed?