Question

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is 1.57 hours. What is density of the planet? Assume that the planet has a uniform density.

Answer 1

The  of the planet is $2249.17 \frac{kg}{m^3}$

Solution:

Given

Time period T = 1.57 hours = $1.57 \times 60 \times 60 sec$

using formula

T = $\frac{2 \times \pi}{ \omega}$

$\omega = \frac{2 \pi} T\\\omega = \frac{2 \pi} {1.57 \times 60 \times 60 sec}$

also, force $F = \frac{GMm}{R^2}$

meanwhile Force $F = \frac{mv}{R^2}$

equating both the above equations we get

we get $v = \sqrt{\frac{GM}{R} }$

also $M = \frac {4\pi R^3 \rho} 3$

also, $\omega = \frac vR$

then $\frac{2 \pi} {1.57 \times 60 \times 60 sec} = \sqrt{\frac{G \frac {4\pi R^3 \rho} 3}{R} }$

solving the equation we get

$\rho = 2249.17 \frac{kg}{m^3}$

What is density?

• The substance's mass per unit of volume is known as its density (volumetric mass density or specific mass).
• The Latin letter D can also be used to represent density, however, the Greek character rho is more frequently used. Density is mathematically defined as mass divided by volume.
• The density of a pure substance is equal to its mass concentration in numbers. Density varies widely among materials and may be important in relation to packaging, purity, and buoyancy.
• The densest known elements under conditions of normal temperature and pressure are osmium and iridium.

To know more about Density  with the given link

brainly.com/question/15164682

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