If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? Please show your work.

If a spacecraft was parked on Venus and needed to make a flight to Jupiter, it would need to travel 670,338,270 km.

Explanation:

Jupiter - Various Properties

Jupiter Meaning:

Jupiter is the largest planet in the solar system. Fittingly, it was named after the king of the gods in Roman mythology. In a similar manner, the ancient Greeks named the planet after Zeus, the king of the Greek pantheon.

Jupiter is a gas giant that is the 5th planet from the sun. It is known as the biggest planet in the solar system. It is a very marvelous planet regarding the characteristics of the atmosphere and “surface” of the planet.The planet is a gas giant, so the whole planet that could’ve been the crust and the mantle is full of poisonous gases. Except for the core, it is full of rocky metals. The planet Jupiter has approximately 70 moons. Jupiter has a high gravitational pull, so it can easily grasp some satellites or other rocky bodies into its collection.Jupiter’s distance from the sun is 483.8 million miles.It’s orbital period is 12 earth years.Jupiter’s length of a day is 9 hours and 56 minutes.Jupiter has a radius of 43,441 miles.Has a gravity of 24.79 m/s squared.

Venus - Various Properties

It's very hot. It has a thick dense atmosphere bloated with strong greenhouse gasses.Its also the second brightest celestial body when viewed from Earth due to its reflective gasses.It is also very volcanically active. From what we know now, Venus has no tectonic plates.Venus is also very similar in size to Earth.

Venus Meaning:

Venus (plural veneres) is the Latin word for ‘loveliness,’ ‘beauty,’ ‘charm,’ It is derived from Proto-Italic *wenos- ('desire'). The ultimate source is the Proto-Indo-European (PIE) *wenh₁-os ('desire').

To calculate how far the spacecraft would need to fly is to calculate the distance betwen Venus and Jupiter.

To save energy, let's consider a Hohmann transfer orbit, an ellipse tangent to opposite sides of Venus's and Jupiter's orbits. The spacecraft would follow the outbound half of this orbit, departing ahead of Venus and arriving as Jupiter overtakes it.

Depending on where in Jupiter's orbit the spacecraft meets it, this orbit has semi-major axis a = (rV + rJ) / 2 = 2.96±0.03 au and period of a3/2 = 5.10±0.08 years. The outbound half has a path length of 7.78±0.07 au and takes 2.55±0.04 years. As Jupiter moves 72° to 84° around the Sun in that time, the launch window is when Venus's heliocentric ecliptic longitude is 96° to 108° behind Jupiter's.

To convert au to km, multiply by 1.496 × 108 km / au.

If a spacecraft was parked on Venus and needed to make a flight to Jupiter, it would need to travel 670,338,270 km.

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