Question

Suppose that you decided to send a spacecraft to Neptune using a Hohmann transfer. The craft starts in a circular orbit close to the Earth (1 AU) and is to end up in a circular orbit near   Neptune (about 30 AU).   (a) How long would the transfer take?   (b) How could you shorten this time, without increasing the amount of fuel required?   (c) What change in velocity is needed to enter the transfer orbit?   (d)   What is the change in velocity needed to enter the circular orbit near Neptune?

Answer 1

(a) The time taken t during the transfer can be obtained by using Kepler's third law as follows

Here, r1= 1AU, r2=30 AU , GM=1.327 x 10 ¹¹ km³/s². Putting all the values in Eq. (1) in S.I units we get

(b) It can be done by using the concept of Gravity assist. If we allow the spacecraft to pass near the Jupiter planet first and then Neptune then by the conservation of momentum because of the large mass of Jupiter spacecraft will start to travel with approximately double of its speed and will take shorter time.

(c)The change in the velocity delta v1 required to transfer can be calculated as

(d) The change in velocity delta v2 needed to enter in Neptune orbit can be given as