A satellite is orbiting a planet with an orbital radius r. Which of the following diagrams represents the direction of the velocity and acceleration of the satellite?Single choice
A
a.
B
b.
C
c.
D
d.
E
e.

Question

A satellite is orbiting a planet with an orbital radius r. Which of the following diagrams represents the direction of the velocity and acceleration of the satellite?

BlackTom AI · Accepted Answer

In uniform circular motion the instantaneous velocity is tangent to the path and the acceleration is centripetal — it points directly toward the center of the circle with magnitude a = v^2/r (or a = ω^2 r).

Step-by-step reasoning:
1. Place the satellite at the leftmost point of the circular orbit. The radius vector from the satellite to the planet’s center points horizontally to the right. 
2. The instantaneous velocity must be perpendicular to the radius vector, i.e., vertically upward at that point (tangent to the circle).
3. The centripetal acceleration (caused by gravity) must point along the radius toward the center, i.e., horizontally to the right. Its magnitude is a = v^2/r but the important feature here is its direction toward the center.
4. Option a shows the blue velocity arrow pointing up (tangent) and the red acceleration arrow pointing right (toward the center). That matches the physical requirement exactly.

Why other choices are incorrect:
- b: shows acceleration pointing left (away from the center) — wrong direction for centripetal acceleration.
- c: swaps the roles so acceleration is upward and velocity left — velocity must be tangent (up) and acceleration must be radial (right), so this is incorrect.
- d: shows velocity pointing right (radial) and acceleration upward (tangential) — incorrect orientation (velocity cannot be radial for circular motion).
- e: shows acceleration at an outward diagonal (not pointing exactly to the center) — centripetal acceleration must be exactly radial toward the center, so a diagonal outward/inward is wrong.

Therefore the correct diagram is a. This matches the provided answer: a.

A satellite is orbiting a planet with an orbital radius r. Which of the following diagrams represents the direction of the velocity and acceleration of the satellite?Single choice

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