Orbital Velocity of Mercury vs Earth

[orwellkid]

Hello all,

I need your help to win a bet here.

Here's the bet:

I say, that the Earth moves faster through space (higher velocity) than Mercury, because our Orbit over the Sun is a higher altitude.

For example, when you are in LEO ~150km, you need a positive prograde burn to increase your velocity to achieve a higher orbit. Is this not the same for planets?

He claims, that Mercury moves faster through space (higher velocity) than the Earth, because it requires more velocity to overcome the greater gravitational force of the Sun.

Who is right? I hope it's not him, or I'm out a pack of smokes. :rofl:

Cheers,

_O.K._

 

[Urwumpe]

You are wrong, because you have not paid attention when playing orbiter.

Mercury travels at roughly 47 km/s, Earth at roughly 29 km/s.

The reason is simple: The gravity force of the sun is stronger the closer you get to it, so you need to be faster to stay in a nearly circular orbit. Just like your smart friend knew. A good moment to consider stopping smoking.

 

[Fizyk]

When you are in LEO, you need one prograde burn to raise apoapsis, and next one to raise periapsis, but the velocity later is... lower. That's because when you're reaching the apoapsis, the gravitational pull of the Earth is slowing you down, more than you need to accelerate to raise periapsis.
So Mercury is indeed moving faster - about 47 km/s if I remeber it correctly, while Earth has velocity of about "only" 30 km/s.

EDIT: Heh, Urwumpe was first

 

[orwellkid]

I really really really feel like an *******.

*sigh*

Cheers. Thanks for the info.

 

[dbeachy1]

Orwellkid, don't feel too bad -- while Earth does orbit the sun slower than Mercury, Earth does in fact have more orbital energy than Mercury: orbital energy = kinetic energy (related to mass and orbital velocity) plus potential energy (related to mass and the planet's position in orbit around the sun). So while Mercury does have more kinetic energy (motion), a spacecraft has to lose kinetic energy to reach it from Earth, at which point the spacecraft converts potential energy into kinetic energy as it falls toward the Sun.

In a nutshell, ranking planets by their orbital velocity alone is missing the other half of the equation. So I think you could make a case for only losing half a pack of smokes.

 

[orwellkid]

God bless you Merry Gentleman.

This is EXACTLY what I was thinking... however I was getting energy confused with velocity. Based on wording, however, I feel I will lose this bet. But thanks for that tidbit... I knew I couldn't be COMPLETELY retarded. :rofl:

Cheers bud... you are a hero!

_O.K._

 

[simonpro]

Orbital energy of mercury: 1.128e+33
Orbital energy of Earth: 7.947e+33

 

[mjessick]

Orbital energy of mercury: 1.128e+33
Orbital energy of Earth: 7.947e+33

This isn't very useful without units, or the correct algebraic signs.

 

[simonpro]

This isn't very useful without units, or the correct algebraic signs.

I'm not writing all that x10e crap as most of the world isn't taught to do that. I didn't write units because I couldn't be bothered. Next question?

 

[mjessick]

Not mentioning the units means it isn't obvious that you multiplied the more usual specific (per mass) energy by the mass to get a Joules type number.

Getting the sign wrong (the numbers should be negative) and not mentioning the "reference frame" (in this case, referenced to zero as the energy level to escape the Sun) means that the conclusion one might draw from the number is likely wrong.

Just looking at the number gives the impression that the Earth has more energy than Mercury, when actually it would take 7 times more energy to escape the Earth than it would to cause Mercury to escape.

 

[simonpro]

mentioning the units means it isn't obvious that you multiplied the more usual specific (per mass) energy by the mass to get a Joules type number.

If I wanted specific energy I would've said specific energy. As I didn't then it's fair to assume that I didn't mean specific energy. Or perhaps I should start listing velocities as accelerations

Getting the sign wrong (the numbers should be negative) and not mentioning the "reference frame" (in this case, referenced to zero as the energy level to escape the Sun) means that the conclusion one might draw from the number is likely wrong.

Both of these were evident from Reverend's posts. As I've already said I couldn't be bothered with the specifics. If you want to be pedantic then that's your own problem.

Just looking at the number gives the impression that the Earth has more energy than Mercury, when actually it would take 7 times more energy to escape the Earth than it would to cause Mercury to escape

Well done.