# Watching Earth travel in space...what should be the location

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1. Nov 17, 2015

### abhaybakshi

Dear All,

Is it possible to watch earth orbiting the sun in space like we watch a car coming towards us on a highway ?
I mean, I would like to see it coming towards my spaceship at the rate of say 50 km/hr.

Now some questions -
1. What should be my location and speed of my spacecraft
2. Will I see that earth is rotating around itself as well ?

I had this question since long but could not find answer even on internet or any other forum.

-Abhay

2. Nov 17, 2015

### willem2

The location of your spaceship could be anywhere, and its speed should be 50 km/h towards the earth.
You will have to use your engines to maintain the speed however. If you're too close to the earth, you will fall towards it, and if you're far enough away to not fall towards it, you will be in a different orbit around the sun, and this will most likely result in going further away from the earth eventually.
An orbit like that of the asteroid Cruidne is possible/ https://en.wikipedia.org/wiki/3753_Cruithne

You can always detect the rotation from the earth. Even if you move so that you'll always be above the same point on the surface, you can detect that one side has a speed more towards you and the other side has a speed more away from you.

3. Nov 17, 2015

### Janus

Staff Emeritus
Let's work out some figures. Let's say that you are starting out your observation of the Earth while it has the same apparent size as the Moon appears from the Earth. This puts you some 1.4 million km from the Earth.
Let's put you ahead of the Earth in it's orbit and moving at 50 km/hr slower than the Earth around the Sun. There are going to two influences on you, One is the gravity of the Earth pulling you towards it, and the other the Sun's influence on you. At first, the Sun's influence will be greater and as a result, because you are moving slower than the required speed to maintain a circular orbit at this distance from the Sun, you will begin to drift towards the Sun (we will, for the sake of simplicity, assume that the Earth itself is in a circular orbit). If we ignored any future influence from the Earth, you would be in an elliptical orbit that dips in ~360,000 km closer to the sun than the Earth's orbit before returning to Earth orbit distance.

But the Earth is there and as it gets closer, it will have a stronger and stronger influence on you, pulling you towards it more and more. Of course, since you are ahead of the Earth in its orbit, your tendency to move towards it faster and faster, means you are also moving slower and slower with respect to the Sun, which increases your tendency to fall in towards the Sun. Whether or not this will be a strong enough tendency to prevent you from hitting the Earth is not something we need to work out here.

So, as willem2 has already alluded to, you will need to apply some type of thrust for your ship to maintain your 50 km/h speed with respect to it. There are a couple of ways to handle this. The first is to put you in Earth's orbital path as above and use your engines to cancel out both the Sun's and Earth's Gravity influence. The Second is to start in a position ahead of and slightly further from the Sun than the Earth is, so that the Sun's influence tends to causes your paths to intersect. (you'll still need to use your engines to counter Earth's gravity.)

That all being said, and assuming you have now worked out how you are going to maintain a constant velocity of 50 km/hr towards the Earth, what would you see?

You start off with the Earth 1.4 million km away and looking the size that the Moon looks to us now. It will take something over 3 yrs to close that 1.4 million km distance at 50 km/hr. To you, the Earth would seem not to be noticeably moving at all. (even at 100 km above the ground, you would be hard pressed to visibly notice the motion.) You would also definitely note the Earth's rotation, as it would complete over 1100 rotations in that 3+ years.

4. Nov 18, 2015

### abhaybakshi

Excellent Janus ... thanks I can imagine a bit what you are saying !!

Yes, the earth's orbit around sun is too complex and there are around 5-6 different types of velocities to consider. For example, earth orbit is not circular, sun is also moving in certain direction itself, and then whole milky way galaxy is also moving. So it will be very complex maneuvers that the spacecraft has to make to keep it ahead in earth's orbit and waiting for earth to arrive there !!

I guess our spacecraft will need multi-directional thrusts firing simultaneously to keep it steady at a point we desire.

What happens then if if we put our spacecraft at L1 ? Will it be more fuel efficient approach ?

5. Nov 18, 2015

### Janus

Staff Emeritus
The solar system's motion through the galaxy and the galaxy's motion with respect to other galaxies are a non-issue, since these motions are already shared by our ship. (there is no such thing as absolute motion with respect to space, so we only need to concern ourselves with the relative motion between our craft and the major bodies who's gravity makes a significant effect
No, once you work out the net effect of all the influences involved you just need to have to thrust in one direction to counter this net effect. The direction and amount of thrust will change as the distance from the Earth changes, but it still only needs to be in one direction.
Difficult to say at first glance. While at L1 you are maintaining a constant distance from the Earth because of a balance of forces, but once you leave it, that balance goes away and now you have to factor in the unbalance. You'd likely have to crunch some numbers to determine which approach would be the most fuel efficient. It becomes a three body problem to which there is no direct solution. (L1 itself is an exception to this, but you move away from it you lose the direct solution.)