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Find the mass (in kg) of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 108 m and its period is 2.52 days. How many Earth masses is this? Part 1 of 3 In order to find the mass, we need to combine the formulas for circular velocity and speed of the moon in its orbit. 2πr P GM V = Setting them equal gives: V = M = Squaring both sides and solving for mass: GM (2πr) ² 47² GM 2πr Vr P Find the mass of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 10³ m and its period is 2.52 days. Once you solve for the mass, does the exponent of the radius change? What is the exponent for r? G (rm) 2x ! (P)²

Find the mass (in kg) of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 108 m and its period is 2.52 days. How many Earth masses is this? Part 1 of 3 In order to find the mass, we need to combine the formulas for circular velocity and speed of the moon in its orbit. 2πr P GM V = Setting them equal gives: V = M = Squaring both sides and solving for mass: GM (2πr) ² 47² GM 2πr Vr P Find the mass of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 10³ m and its period is 2.52 days. Once you solve for the mass, does the exponent of the radius change? What is the exponent for r? G (rm) 2x ! (P)²

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Find the mass (in kg) of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 108 m and its period is 2.52 days. How many Earth masses is this? Part 1 of 3 In order to find the mass, we need to combine the formulas for circular velocity and speed of the moon in its orbit. 2πr P GM r V = Setting them equal gives: V = M = 47² G GM r Squaring both sides and solving for mass: GM - (2x)² (2⁰ r) = = Find the mass of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 108 m and its period is 2.52 days. Once you solve for the mass, does the exponent of the radius change? What is the exponent for r? (rm) 2πr P 2 X ! (PS)²
Transcribed Image Text:Find the mass (in kg) of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 108 m and its period is 2.52 days. How many Earth masses is this? Part 1 of 3 In order to find the mass, we need to combine the formulas for circular velocity and speed of the moon in its orbit. 2πr P GM r V = Setting them equal gives: V = M = 47² G GM r Squaring both sides and solving for mass: GM - (2x)² (2⁰ r) = = Find the mass of Uranus from the orbital parameters of its moon, Ariel. The radius of Ariel's orbit about Uranus is 1.91 x 108 m and its period is 2.52 days. Once you solve for the mass, does the exponent of the radius change? What is the exponent for r? (rm) 2πr P 2 X ! (PS)²
We first need to convert the period from days to seconds. (Pdays)(Ns/day) Ps Ps S = = S
Transcribed Image Text:We first need to convert the period from days to seconds. (Pdays)(Ns/day) Ps Ps S = = S
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