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geniusboy
1 month ago
14

A satellite that weighs 4900 N on the launchpad travels around the earth's equator in a circular orbit with a period of 1.667 h.

The earth's mass is 5.97 × 1024 kg, its equatorial radius is 6.3 × 106 m, and G = 6.67 × 10-11 N • m2/kg2.
a. Calculate the magnitude of the earth's gravitational force on the satellite.
b. Determine the altitude of the satellite above the Earth's SURFACE.
Physics
1 answer:
Softa [3K]1 month ago
4 0

Answer:

(a)F= 3.83 * 10^3 N

(b)Altitude=8.20 * 10^5 m

Explanation:

The weight at the launchpad corresponds to the gravitational force acting between the Earth and the satellite.

W = GMm/R²

where R denotes the radius of the Earth.

Rearranging the equation yields:

WR² / GM = m

From this, we find: m = 4900 * (6.3 * 10^6)² / (6.67 * 10^-11 * 5.97 * 10^24) = 488 kg

To maintain the satellite's circular orbit radius (r), the required centripetal force (Fc) is described by:

Fc = mω²r

where ω represents the angular velocity in radians per second. The satellite completes one full revolution (2π radians) in 1.667 hours.

Thus, ω = 2π / (1.667 * 60 * 60) = 1.05 * 10^-3 rad/s

In orbit, at a distance (r) from the center of the Earth, centripetal force (Fc) is provided by the gravitational interaction between the Earth and the satellite:

Fc = GMm/r²

By equating mω²r to GMm / r², we obtain:

ω²r = GM / r²

Therefore, we can derive r³ = GM/ω² = (6.67 * 10^-11 * 5.97 * 10^24) / (1.05 * 10^-3)²

r³ = 3.612 * 10^20

Hence, r = 7.12 * 10^6 m

(a) F = GMm/r²  

F=(6.67 * 10^-11 * 5.97 * 10^24 * 488) / (7.12 * 10^6 )²

F= 3.83 * 10^3 N

(b) The altitude is calculated as: altitude = r - R = (7.12 * 10^6) - (6.3 * 10^6) = 8.20 * 10^5 m

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