# Simple gravity question

• cookant

#### cookant

Hi,
I'm new to this and trying to explain gravity to a 10 year old ! My question is..

If I was floating in space on directly the opposite side of the sun to earth, in the same orbit as earth...would Earth eventually catch me up ? if not (as I thought everything in the same orbit moves at the same velocity), how would a planet clear its orbit...

I read somewhere about the 'perception' of gravity being that it pulls you down, but if you were an observer in space you'd see it was the Earth accelerating into you..so trying to figure out whether I understood that correctly...

thanks,
Ant.

If I was floating in space on directly the opposite side of the sun to earth, in the same orbit as earth...would Earth eventually catch me up ? if not (as I thought everything in the same orbit moves at the same velocity), how would a planet clear its orbit...

No, the Earth would not catch up to you, as you both would be moving at the same speed.
I can't answer how planets clear their orbits, sorry.

The Earth goes around the sun at 67,000 miles per hour. It will be moving towards you. You can guess how it clears it orbit (splat). If you are moving at the same velocity you will continue (to a first order) to orbit on opposite sides of the sun.

Gravity manifests itself as an attractive force between two masses that is inversely proportional to distance squared. The force between you and the Earth manifests itself as your weight. The force of gravity will cause you to accelerate at 32 ft/s2 (neglecting air friction) if you are falling.

Your weight is the gravitational force between you and the Earth acting on your mass. In fact weight is actually in units of force.

When you jump off a cliff, is the Earth rushing towards you? Same thing in space (ignoring orbital stuff). Who is rushing where is in the eyes of the beholder, but in reality you are not changing the Earth's obit much.

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Hi cookant, welcome to PF!

For clarity's sake, let's imagine all orbits are circular.

The Earth orbits the Sun at the particular distance and velocity that it does, due to the gravitational force exerted on it by the Sun's mass towards the centre of the orbit(the force of gravity equals centripetal force).
If the force towards the centre were higher, it'd have to orbit at a closer orbit and higher velocity. It could not stay in its present orbit.

Now, imagine you were in the same orbit(the same distance from the Sun) and opposite the Earth. You'd be attracted gravitationally towards both the Sun and the Earth along the same line. This means that the acceleration you'd experience would be higher than that the Earth does(your mass being negligible it feels only the Sun's gravitational field), so you would be inevitably pulled into a tighter orbit.

In a tighter orbit, you'd orbit faster, and after a number of revolutions you'd catch up with Earth. The changing gravtitational interactions would then most likely fling you onto some other orbit.

To stay directly opposite the Earth, you'd need to orbit the Sun at a bit farther distance, so that the higher mass pulling you in would be offset by the increase in distance(gravity falls with the square of the distance).
This point with relation to the Sun and the Earth is called the Lagrangian point L3, and along with the remaining four(http://en.wikipedia.org/wiki/Lagrangian_point) is a special solution to the otherwise extremely difficult to solve "three body problem"(i.e., how three gravitating bodies interact over time).

It is also an ustable one, due to the fact that there are many other massive bodies in the solar system, many of which passing by closer than the distance to Earth from that point(which would be over 2 AU).

The perturbations by the many planets in the solar system help clear the orbits, but some material tends to stay around in the more stable L4 and L5 regions. These are called Trojans, and are especially prominent in the case of Jupiter(http://en.wikipedia.org/wiki/Jupiter_trojan).

As for the perception of gravity, in our everyday experience it's what we call the surface of the Earth pushing against our feet, or bums, of faces should we trip, etc. In space, the largely uniform gravitational field would accelerate you while not producing any sensory reaction at all. You'd be in free fall and feel completely weightless even as you're hurtling towards whatever at many kilometres per second.

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Ohh, I was unaware of that, Bandersnatch. Thanks for correcting me.

To highlight the important point Bandersnatch mentioned: there is a single point on the opposite side where you could orbit , but it is unstable - every deviation from this point (and the exact speed and direction) leads to large deviations in the orbit over time. In geological timescales (millions to billions of years), those deviations will likely lead to a close approach with Earth at some point - either a collision or a significant orbital change.

Hi cookant, welcome to PF!

Now, imagine you were in the same orbit(the same distance from the Sun) and opposite the Earth. You'd be attracted gravitationally towards both the Sun and the Earth along the same line. This means that the acceleration you'd experience would be higher than that the Earth does(your mass being negligible it feels only the Sun's gravitational field), so you would be inevitably pulled into a tighter orbit.

ahhhhhhh! Thank you very much

thanks for the responses guys, this is a very dangerous forum for someone like me with lots of questions ;-) ...I'll be back !

Ant.