Satellite synchronous to Venus' rotation

[endeavor]

Venus has a rotational period of 243 days. What would be the altitude of a syncom satellite for this planet?

I am pretty sure a syncom satellite is a satellite that orbits synchronously to the rotation of the planet.

I don't know how to solve this problem... help

 

[berkeman]

Think about what things affect how long it takes a satellite to go around in an orbit. And think about the basics of uniform central motion (something going in a circular path). What is the centripetal (sp?) acceleration that causes a mass to go around in a circle? How is that centripetal acceleration related to the speed of the mass? Now what is generating that force in the case of a satellite? What about Venus affects the centripetal acceleration of the satellite?

 

[endeavor]

a_c = v²/(R_V + h)
but i don't know a_c, v, or h...
v = squareroot of (G * M_V / (R_V + h))
but i still don't know v or h...

I found that the distance from venus to the sun is 108.2 * 10^9 m, so I figured that's 3.0 * 10^9 m/day. That means every day venus travels 3.0 * 10^9 m. Therefore the circumference of venus is 3.0 * 10^9 m? But that's not right...

I'm still not sure how I'm supposed to solve this...

 

[SpaceTiger]

a_c = v²/(R_V + h)
but i don't know a_c, v, or h...
v = squareroot of (G * M_V / (R_V + h))
but i still don't know v or h...

How might one express the velocity of the satellite in terms of the radius of the orbit and the period?

Hint: What is the shape of the orbit have to be for it to be synchronous? What does this say about how the satellite's speed changes throughout its orbit?

 

[endeavor]

v = (2pi * r)/ T, where T is the period

I have
r = 6052000m + h, where h is the altitude
T=?
To find h, I would have to know v already...

The satellite has to orbit in a circle, and therefore it's speed doesn't change.

 

[Smilecdl]

T=?

You know T it is defined in your question...for the Earth T would be 24 hours so what is it for Venus? [Don't forget to change you units to seconds when doing the final calculation]

 

[SpaceTiger]

The satellite has to orbit in a circle, and therefore it's speed doesn't change.

Good, and what is the other condition for it to be synchronous?

 

[endeavor]

Okay, I finally got the right answer...
I thought 243 days meant that Venus has 243 days in its path around the sun.
Venus and the satellite have to have the same angular speed.
w=v₂/(r + h)
I also have the equation for the speed of a satellite:
v₂=square root of (GM_V/(r + h))

Solving for the two unknowns, v₂ and h, I get h = 1.53 * 10^9 m, which is the correct answer.

Thanks for all the great help! I really appreciate it!

 

[physhater]

Sorry, can you explain how you solved for v and then for h? I can see how it would be easy solving for the altitude once you know the v, but I don't know how to get to that.