Question

A satellite orbits Mars. When it reaches S, it is about 12,000 km above the planet. How many arc degrees of the planet are visible to a camera in the satellite?

Answer 1

The camera in the satellite can see approximately 1680.87 degrees of Mars.

Step-by-step explanation:

The number of arc degrees visible to a camera in the satellite can be determined by calculating the angle subtended by the distance between the satellite and Mars with respect to the center of Mars. To calculate this, we can use the formula:

Angle in degrees = (Distance between satellite and Mars / Radius of Mars) × 360 degrees

Given that the satellite is 12,000 km above Mars, we need to add this distance to the radius of Mars, which is approximately 3,389.5 km. Thus, the distance between the satellite and the center of Mars is 15,387.5 km. Plugging these values into the formula:

Angle in degrees = (15387.5 km / 3389.5 km) × 360 degrees = 1680.87 degrees

Therefore, approximately 1680.87 degrees of Mars are visible to the camera in the satellite.

Answer 2

The equatorial radius of the planet Mars:
r = 3.396 km
An arc of the planet that is visible to a camera in a satellite:
cos Ф/2 = r / ( r + 12,000 ) = 3.396 / ( 3,396 + 12,000 ) =
= 3,396 : 15,396 = 0.22
Ф/ 2 = cos^(-1) 0.22 = 77.3°
Ф = 2 · 77.3° = 154.6°
Answer: 154° 36 `