QuestionMay 30, 2025

A satellite (mass 500 kg) orbits a planet (mass6times 10^wedge 24kg) at a distance of 7times 10^wedge 6m What is the gravitational force between them?(Use the desmos calculator to solve) F=(Gm_(1)m_(2))/(r^2) (Use the gravitational constant G=6.674times 10^-11Ncdot m^2/kg^2) (1 point) 2.04times 10^4N 4.76times 10^4N 4.08times 10^3N 3.43times 10^3N

A satellite (mass 500 kg) orbits a planet (mass6times 10^wedge 24kg) at a distance of 7times 10^wedge 6m What is the gravitational force between them?(Use the desmos calculator to solve) F=(Gm_(1)m_(2))/(r^2) (Use the gravitational constant G=6.674times 10^-11Ncdot m^2/kg^2) (1 point) 2.04times 10^4N 4.76times 10^4N 4.08times 10^3N 3.43times 10^3N
A satellite (mass 500 kg) orbits a planet (mass6times 10^wedge 24kg) at a distance of
7times 10^wedge 6m What is the gravitational force between them?(Use the desmos
calculator to solve)
F=(Gm_(1)m_(2))/(r^2)
(Use the gravitational constant G=6.674times 10^-11Ncdot m^2/kg^2)
(1 point)
2.04times 10^4N
4.76times 10^4N
4.08times 10^3N
3.43times 10^3N

Solution
4.2(284 votes)

Answer

4.08 \times 10^3 \, \text{N} Explanation 1. Identify the given values m_1 = 500 \, \text{kg}, m_2 = 6 \times 10^{24} \, \text{kg}, r = 7 \times 10^6 \, \text{m}, G = 6.674 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2. 2. Apply the gravitational force formula Use **F = \frac{G m_1 m_2}{r^2}** to calculate the force. 3. Calculate the force Substitute the values: F = \frac{(6.674 \times 10^{-11}) \times (500) \times (6 \times 10^{24})}{(7 \times 10^6)^2}. 4. Simplify and compute Compute the numerator: 6.674 \times 10^{-11} \times 500 \times 6 \times 10^{24} = 2.0022 \times 10^{16}. Compute the denominator: (7 \times 10^6)^2 = 4.9 \times 10^{13}. Divide: F = \frac{2.0022 \times 10^{16}}{4.9 \times 10^{13}} = 4.08 \times 10^3 \, \text{N}.

Explanation

1. Identify the given values<br /> $m_1 = 500 \, \text{kg}$, $m_2 = 6 \times 10^{24} \, \text{kg}$, $r = 7 \times 10^6 \, \text{m}$, $G = 6.674 \times 10^{-11} \, \text{N}\cdot\text{m}^2/\text{kg}^2$.<br /><br />2. Apply the gravitational force formula<br /> Use **$F = \frac{G m_1 m_2}{r^2}$** to calculate the force.<br /><br />3. Calculate the force<br /> Substitute the values: $F = \frac{(6.674 \times 10^{-11}) \times (500) \times (6 \times 10^{24})}{(7 \times 10^6)^2}$.<br /><br />4. Simplify and compute<br /> Compute the numerator: $6.674 \times 10^{-11} \times 500 \times 6 \times 10^{24} = 2.0022 \times 10^{16}$.<br /> Compute the denominator: $(7 \times 10^6)^2 = 4.9 \times 10^{13}$.<br /> Divide: $F = \frac{2.0022 \times 10^{16}}{4.9 \times 10^{13}} = 4.08 \times 10^3 \, \text{N}$.
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