This question and the list of answer-choices were written by somebody who is unclear on the concepts, and has no business being involved with teaching Physics. This is not harmless. It's misleading to any student who is trying to make sense of it, and perhaps also to his Physics teacher.
The writer of this question thinks that 'acceleration' means speeding up.
IT DOESN'T !
'Acceleration' means ANY change of speed OR DIRECTION. Speeding up, slowing down, and turning or curving are all 'acceleration'.
An object moving with constant speed is still accelerating if it isn't moving in a STRAIGHT LINE, because its direction keeps changing.
An object moving with constant speed in a circle is experiencing an acceleration that is directed toward the center of the circle. Its magnitude is
(the object's speed)² divided by (the radius of the circle) .
It's called "centripetal acceleration".
Going through the choices . . .
<em>a). Its acceleration is zero since it is moving at constant speed.</em> NO. Speed is not the only thing that determines acceleration.
b). Its acceleration is not zero but is very small. What does "very small" mean ? Could it be small without being very small ? What are the numbers for acceleration that would be called 'small', 'very small', and 'not small' ? This choice could not legitimately be the answer to anything.
<em>c). Its acceleration is 9.8 m/s²</em>. NO. That number is the acceleration of things that fall down on the Earth. It's the acceleration that results from Earth's gravity on the surface. It points toward the center of the Earth. It's not related to the Earth's centripetal acceleration in orbit.
We could stop here. The question only wants us to say which choice is "most correct", and we already know that a)., b)., and c). are all definitely NOT correct. So if there IS a correct one, it'll have to be d). But this is a sleazy way out. We're honorable people, so we have to continue, and see what the deal is with choice-d).
<em>d). Its acceleration is 1.0 m/s²</em>. Maybe it is, and maybe it isn't. I suspect it isn't, because it would be a huge coincidence if it happened to be exactly this number. But there's no way to know without calculating it.
Centripetal acceleration = (speed)² / radius
Radius of the orbit = 93 million miles
Speed = one circumference per year
This is gonna be a #%$&@ to calculate ... we have to convert everything to consistent units. I'll tell you what: YOU just relax, and I'LL do the work.
Radius = (93 x 10⁶ miles) · (1609 meters/mile) = 150 gigameters (not exact, but close enough for right now; I only have to find out whether the acceleration is anywhere close to 1.0 m/s², to find out whether choice-d). is any good at all.)
Circumference = (2π) · (radius) = 9.4 x 10¹¹ meters
Speed = (1 circumference/year) = (9.4 x 10¹¹ meters) / (365 days)
Speed = (9.4 x 10¹¹ meters / 365 days) · (1 day / 86,400 seconds)
Speed = (9.4 x 10¹¹ / 365 · 86,400) (meters-days / days-seconds)
Speed = 2.98 x 10⁴ meters/sec
OK. I'm seeing light at the end of the tunnel.
[Centripetal] acceleration = (speed)² / (radius)
Acceleration = (2.98 x 10⁴ m/s)² / (150 x 10⁹ meters)
Acceleration = (8.89 x 10⁸ m²/s²) / (150 x 10⁹ meters)
Acceleration = (8.89 x 10⁸ / 150 x 10⁹) (meters² / second-meters)
Centripetal Acceleration = 0.0059 m/s²
And there you have it. I'll admit that I did a lot of rounding and approximating on the way. But unless my answer is at least 100 times too small, choice-d). is as worthless as the other three choices listed.
So I'm going to say that even though choice-d) is technically the 'most correct', that's only because the other three choices are so terrible. The only nice thing you can say about choice-d) is that maybe it's the least bad of all the choices. But it's still poor, and seriously misleading.
<em>None of the choices describes the Earth's motion in its orbit</em>. <em>The correct answer to the question is not included </em>among the choices. The question itself is almost certainly based on a fundamental misunderstanding of the underlying concept of acceleration.
So there !
This is not your fault, Jenny ! I'm grateful to you for the generous bounty of 5 points. And the green crusts and tepid cloudy water were also delicious.
