# Homework Help: Satellite and the Earth

1. Aug 22, 2016

### Vibhor

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I think if the astronaut can somehow throw it behind himself, against the direction of orbital motion ( 180° opposite ) such that the total orbital velocity of the nut is cancelled , it should fall straight down . But this is practically not possible .

Another way is to throw it backwards at an angle such that the velocity vector points towards earth .

I am not really sure with the above reasoning .

Any sincere help is appreciated .

Thanks

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2. Aug 22, 2016

### Filip Larsen

Indeed not practical if he has to cancel all orbital speed, but could less do it?

Perhaps you can find some equations that relates orbital speed and orbital radius?

3. Aug 22, 2016

### haruspex

But it is not necessary to get it into a circular orbit with radius equal to that of Earth. It is only necessary that its orbit intersects Earth's surface. Not sure how hard it is to solve that.

4. Aug 22, 2016

### Vibhor

hi haruspex ,

If you were the astronaut in the problem , what would you do ?

5. Aug 22, 2016

### Staff: Mentor

Ignoring the atmosphere you need only alter the orbit of the nut so that its perigee coincides with the Earth's surface.

If the atmosphere is not to be ignored and you're not in any great hurry to land the nut, then having the perigee dip into the atmosphere will eventually decay the orbit.

So a big hint would be: Find the required ΔV that would lower the perigee of the nut accordingly.

6. Aug 22, 2016

### Vibhor

Hi gneill

Are you suggesting that a decrease in speed would change the orbit from circular to elliptical such that the perigee just touches the surface ??

Sorry .I did not understand .

But even if ΔV is calculated , the astronaut needs a way to implement the change in speed . Would you agree he needs to throw the nut backwards in opposite direction such that the required change in speed is achieved??

7. Aug 22, 2016

### Staff: Mentor

Yes.
What happens to an object moving through air, especially at high speeds? What forces does it encounter? What are the results?
Sure.

8. Aug 22, 2016

### Vibhor

Ok .

Doesn't the angle at which the nut is thrown of any significance ?

9. Aug 22, 2016

### Staff: Mentor

Yes. The details of the "new" orbit depends upon the particulars of the ΔV and the resulting new velocity vector. But the most efficient way to lower the perigee is to direct that ΔV opposite to the original velocity of the circular orbit.

Edit: You might want to look up "Hohmann Transfer Orbit".