On a date when the earth was 147.4x106 km from the sun, a spacecraft parked in a 200 km altitude circular earth orbit was launched directly into an elliptical orbit around the sun with perihelion of 120x106km and aphelion equal to the earth’s distance from the sun on the launch date. calculate the ∆v required and v[infinity] of the departure hyperbola.

ΔV =  

Explanation:

Distance of earth from sun =

Spacecraft perihelion =

gravitational parameters are now given as

radius of earth  = 6378 Km

Heliocentric spacecraft velocity at earth sphere of influence =

Heliocentric velocity of earth =

assume

Geometric spacecraft velocity of spacecraft at perigee of departure hyperbola

geometric space craft velocity in its circular parking orbit

              ΔV =  

the clapeyron equation (also called the clausius-clapeyron equation) relates the slope of a reaction line on a phase diagram to fundamental thermodynamic properties.

explanation: