Interplanetary Travel. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel2 Interplanetary Travel Planning for Interplanetary Travel Planning a Trip

Interplanetary Travel

Unit 2, Chapter 6, Lesson 6: Interplanetary Travel 2

Interplanetary Travel Planning for Interplanetary

Travel Planning a Trip through

the Solar System Interplanetary

Coordinate Systems

Gravity-assist Trajectories Helping Spacecraft

Move Between Planets

Unit 2, Chapter 6, Lesson 6: Interplanetary Travel SECTION 6.1 3

Planning a Trip Through the Solar System

Using the Hohmann Transfer, we saw how to transfer between two orbits around the same central body, such as Earth.

Interplanetary transfer just extends the Hohmann Transfer. Central body is the Sun. Departure and destination planets are vital.


Interplanetary Coordinate Systems

In the two-body problem described earlier in the course: Only two bodies are acting—the spacecraft

and the Earth. Earth’s gravity is the only force acting on

the spacecraft.

We used the geocentric-equatorial coordinate system.


Interplanetary Coordinate Systems (cont’d)

For interplanetary travel, as a spacecraft goes farther away, Earth’s pull becomes secondary to the Sun’s.

Because the Sun is the central body, we must develop a Sun-centered—or heliocentric—coordinate system.


Interplanetary Coordinate Systems (cont’d)

Heliocentric-ecliptic coordinate frame Origin: the Sun Basic plane: the

ecliptic plane (Earth’s orbital plane around the Sun)

Main direction: fixed with respect to the universe “I” axis points to constellation Aires


Forces Acting on an Interplanetary Spacecraft

Four bodies are involved:

Sun Departure Planet Target Planet Spacecraft


Four-body Problem

Analyzing the forces from all three central bodies on the spacecraft would amount to a “four-body” problem.

Too much to handle—the two-body problem was challenging enough.

What can we do to simplify? Break into familiar, manageable pieces. Consider as three two-body problems.


Patched Conic Approximation

Separate four-body problem into three distinct two-body problems.

Deal with gravity between the spacecraft and each large body (Sun and two planets) separately.

FGrav(Sun)FGrav(departure planet)

FGrav(target planet)


Regions of the “Patched Conic”

Region 1: Heliocentric Transfer Orbit Origin: Sun Transfer: Earth to

target planet


Regions of the “Patched Conic” (cont’d)

Region 2: Escape from Departure Planet Origin: Departure

planet Transfer: Earth

departure Patched to region 1


Regions of the “Patched Conic” (cont’d)

Region 3: Arrival at Target Planet

Origin: Target planet Transfer: Arrival at the target planet Patched to region 1


Spheres of Influence

A body’s sphere of influence (SOI) is the surrounding volume in which its gravity dominates a spacecraft. In theory, SOI is infinite. In practice, as a

spacecraft gets farther away, another body’s gravity dominates.


Spheres of Influence (cont’d)

The size of a planet’s SOI depends on: The planet’s mass How close the planet is to the Sun (Sun’s

gravity overpowers that of closer planets). Earth’s SOI

About 1,000,000 kilometers radius If the Earth were a baseball, its SOI would

extend 78 times its radius or 7.9 meters (26 feet).


Spheres of InfluenceEarth’s SOI in Perspective


Frame of ReferenceAn Earth-bound Example

You’re driving along a straight section of highway at 45 m.p.h.

A friend is following in another car going 55 m.p.h. A stationary observer on the side of the

road sees the two cars moving at 45 m.p.h. and 55 m.p.h., respectively.

Your friend’s velocity with respect to you is only 10 m.p.h.


Frame of ReferenceAn Earth-bound Example (cont’d)

“V” = Velocity


Frame of ReferenceAn Earth-Bound Example (cont’d)

Your friend throws a water balloon toward your car at 20 m.p.h. How fast is the balloon going? What your friend sees (ignoring air drag): it’s

moving ahead of his car at 20 m.p.h. What the stationary observer sees: your friend’s

car is going 55 m.p.h., and the balloon leaves his car going 75 m.p.h.

What you see: the balloon is moving toward you with a closing speed of 30 m.p.h.


Frame of ReferenceAn Earth-Bound Example (cont’d)

“V” = Velocity



This example relates to the patched- conic approximation: Problem 1: A stationary observer watches

your friend throw a water balloon. The observer sees your friend’s car going 55

m.p.h., your car going 45 m.p.h., and a balloon traveling from one car to the other at 75 m.p.h.

The reference frame is a stationary frame at the side of the road.



This example relates to the patched-conic approximation: Problem 2: The water balloon departs your friend’s

car with a relative speed of 20 m.p.h. The reference frame in this case is centered at your

friend’s car. This problem relates to the patched-conic’s Problem 2

(in region 2), where Earth is like your friend’s car, and the balloon is like the spacecraft.



This example relates to the patched conic approximation: Problem 3: water balloon lands in your car!

It catches up to your car at a relative speed of 30 m.p.h. The reference frame is centered at your car.

It’s like the patched-conic’s Problem 3 (in region 3), where the target planet is similar to your car and the balloon is still like the spacecraft.

Unit 2, Chapter 6, Lesson 6: Interplanetary Travel SECTION 6.2 23

Gravity-assist Trajectories

Gravity-assist definition: using a planet’s gravitational field and orbital velocity to “sling shot” a spacecraft, changing its velocity (in magnitude and direction) with respect to the Sun.

Spacecraft Passing Behind a Planet


Gravity-assist Trajectories (cont’d)

As a spacecraft enters a planet’s sphere of influence (SOI), it coasts on a hyperbolic trajectory around the planet.

Then, the planet pulls it in the direction of the planet’s motion, increasing (or decreasing) its velocity relative to the Sun. Spacecraft Passing in Front of a Planet


Gravity-assist Trajectories (cont’d)


Summary

Planning for Interplanetary Travel Planning a Trip through the Solar System Interplanetary Coordinate Systems

Gravity-assist Trajectories Helping Spacecraft Move Between Planets


Next

We’ve practiced describing orbits, orbital maneuvers, and interplanetary travel. Next time, we’ll cover ballistic missiles and launch windows and time.

Documents

Interplanetary Travel. Unit 2, Chapter 6, Lesson 6: Interplanetary Travel2 Interplanetary Travel Planning for Interplanetary Travel Planning a Trip