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## Homework Statement

You may assume circular planetary orbits.

a. Calculate the velocity (relative to Earth) at Earth's orbit of the Hohmann transfer orbit that is tangent to both Earth's orbit and Jupiter's orbit.

b. calculate the minimum velocity necessary to launch a spacecraft from the surface of Earth to Jupiter, ignoring Earth's rotation

c. calculate the minimum velocity necessary to launch a spacecraft from the surface of Earth to Jupiter, including Earth's rotation but ignoring its obliquity

d. calculate the time required for a spacecraft moving along a Hohmann transfer orbit to travel from Earth to Jupiter

e. repeat part (b) for Hohmann transfer orbits to Mercury and Venus.

## Homework Equations

vis viva:

GM(2/r - 1/a)

energy:

KE = 1/2mv^2

PE = -GmM/r

kepler's 3rd law:

P^2 = a^3

## The Attempt at a Solution

a. r = 1 AU = 1.5e11 m

2a = 1 AU + 5.2 AU = 9.2e11 m ... a = 4.64e11 m

plug values into vis viva equation, v_h@Earth = 38651.6 m/s

b. ? energy balance ?

c. ? like (b) with added twist ?

d. a = 3.1 AU, P^2=a^3 ... P = 5.458 yrs, want 1/2 P which is 2.73 years

e. ? same as (b) ?

I think (a) and (d) are correct, but not sure how to set up for parts (b) and (c) (and thus (d))... please help!