what is the mass of the planet?

Question

If a satellite in circular orbit is observed to have a speed of 5620 m/s at a eight of 8.73 x 10^6 m above the surface of a planet of radius 1.02 x 10^7 m, what is the mass of the planet?

Answer 1

the gravitational pull will equal the centripetal force


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centripetal force = m•v²/r

or

centripetal force = (mass of object in orbit) • (its velocity²) / (radius, or distance from center of each body)

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gravitational pull = G • (m1•m2)/r²

or

gravitational pull = ( G(the gravitational constant) • (mass of body being orbited) • (mass of body in orbit) ) / (radius, or distance from center of each body)²

where:

G ≈ 6.67 × 10⁻¹¹ N•m²/kg² (see wikipedia)

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The radius to use is the distance between the two bodies' centers of mass.

So, you have to add the radius of the planet to the height above the planet.

radius = (1.02 × 10⁷ + 8.73 × 10⁶) m

or

radius = 1.893 × 10⁷ m

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so, set the gravitational force = centripetal force

G • (m1•m2)/r² = m2•v²/r

☞Notice the mass of the satellite is on both sides and cancels out.
☞So, the result will be independent of the mass of the satellite.


which becomes:

G • (m1)/r² = v²/r

solve for m1:
m1/r² = v² / (r • G)

or

m1 = (r² • v²) / (r • G)

or

m1 = (r • v²)/G

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substitute in known quantities:

velocity = 5620 ㎧
radius = 1.893 × 10⁷ m
G ≈ 6.67 × 10⁻¹¹ N•m²/kg²

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m1 = (1.893 × 10⁷ m • (5620 ㎧)²) / (6.67 × 10⁻¹¹ N•m²/kg²)

or

┏━━━━━━━━━━┓
┃m1 ≈ 8.964 × 10^24 kg┃
┗━━━━━━━━━━┛


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The End


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I Hope this Helps ❣ ❣

Answer 2

G = 6.67428*10^-11 m^3/kgs^2
MG/R^2 = v^2/R
M = Rv^2/G
M = (1.893*10^7m)(5,620 m/s)^2 / 6.67428*10^-11 m^3/kgs^2
M ≈ 8.958160*10^24 kg
M ≈ 8.958160*10^21 metric tons

This is about 1.500 times the mass of the Earth.

Answer 3

It is 7.35e22kg or roughly about 439,000,000,000 Pounds
Most of the mass of the Earth is in the mantle, most of the rest in the core; the part we inhabit is a tiny fraction of the whole.

Answer 4

Use f=mv^2 / r, and plug in everything to solve for m on your own; this is the centripetal force formula

Answer 5

About as much as my mom. so would my moms mass be the size of the earth if she was not on it?

Answer 6

well i used to kno the weight its like 82 quintillion 600 sextillion or somethin idk MAN my science teacher just told us this yesderday