Chapter 8, Problem 8.30P

How much energy is required to lift a 10 kg rock from the surface of the Earth and place it in a circular orbit just 10 km above sea level? Assume Earth's radius is about 6371 km.

Calculate the surface escape velocities for Mars.  rM = 3.3× 106 m, MM = 6 × 1022 kg).

You are in a spacecraft orbiting Venus.The mass of Venus is 4.87E+24 kg, and its radius is 6.05E+3 km. a) The orbital velocity at the surface of the planet is 7.32E+3 m/s. What is the escape velocity from the surface?b) What is the circular orbital velocity at the height of one-half a Venus radius above the surface?c) At a height of 24 radii above the surface of Venus, what is the circular orbital velocity? d) What is the escape velocity at this height?

Please don't provide handwritten solution .....    Given an elliptical orbit with a perigee of 6500 km and a 60,000 km apogee, find the true anomaly of the spacecraft position when it enters the Van Allen belt at an altitude of 500 km (consider only gravitational forces).

We talk of 11.2 km/s as the escape speed from Earth. Is it possible to escape from Earth at half this speed? At one-quarter this speed? If so, how?

A minimum-energy transfer orbit to an outer planet consists of putting a spacecraft on an elliptical trajectory with the departure planet corresponding to the perihelion of the ellipse, or the closest point to the Sun, and the arrival planet at the aphelion, or the farthest point from the Sun. (Assume the orbital radius of the Earth is 1.50  1011 m, and the orbital radius of Mars is 2.28  1011 m.)   (a) Use Kepler's third law to calculate how long it would take to go from Earth to Mars on such an orbit as shown in the figure above. yr(b) Can such an orbit be undertaken at any time? Yes  or No     Explain.

Haley’s Comet closest approach to the Sun is within 0.570 A.U., and its orbital period is75.6 years.Problem 4.1. What is the semi-major axis of the comet’s orbit?Problem 4.2. How far from the sun will Haley’s comet travel before it starts its returnjourney?

A 2660-kg spacecraft is in a circular orbit 1540 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4500 km above the surface? Express your answer to three significant figures.

A minimum-energy orbit to an outer planet consists ofputting a spacecraft on an elliptical trajectory with the departureplanet corresponding to the perihelion of the ellipse, orclosest point to the Sun, and the arrival planet correspondingto the aphelion of the ellipse, or farthest point from the Sun.(a) Use Kepler’s third law to calculate how long it would taketo go from Earth to Mars on such an orbit. (Answer in years.)(b) Can such an orbit be undertaken at any time? Explain.