Question

Given that the acceleration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars' radius is 3400 km, determine the mass of Mars. please show me how to do this!!!

Answer 1

The equation that is applicable is as follows:
F = G * M * m ÷ r^2 F = G * M * m ÷ r^2 
Weight = m * g 
Weight = F m * g = G * M * m ÷ r^2 g = G * M ÷ r^2 
Now you can determine the mass of the planet. For mars, r = 3,400,000 = 3.4 * 10^6 meters 
0.38 = 6.67 * 10^-11 * M ÷ (3.4 * 10^6)^2 0.38 = 6.67 * 10^-11 * M ÷ 1.156 * 10^13 
3.8 = 6.67 * 10^-11 * M ÷ (3.4 * 10^6)^2 0.38 = 6.67 * 10^-11 * M ÷ 1.156 * 10^13 Multiply both sides by 1.156 * 10^13 
1.156 * 10^13 * 0.38 = 6.67 * 10^-11 * M Divide both sides by 6.67 * 10^-11 
1.156 * 10^13 * 0.38 ÷ 6.67 * 10^-11 = M The answer is approximately 6.586 * 10^22 kg The actual mass of Mars is 6.42 * 10^23 kg. I think the acceleration of gravity on Mars is 3.8 m/s^2 
1.156 * 10^13 * 3.8 ÷ 6.67 * 10^-11 = M The answer is approximately 6.586 * 10^23 kg

Answer 2

Mass of Mars is about 6.4 × 10²³ kg

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Further explanation

Let's recall the Gravitational Force formula:

$\boxed {F = G\ \frac{m_1 m_2}{R^2}}$

where:

F = Gravitational Force ( N )

G = Gravitational Constant ( = 6.67 × 10⁻¹¹ Nm²/kg² )

m = mass of object ( kg )

R = distance between object ( m )

Let us now tackle the problem!

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Given:

acceleration of gravity at the surface of Earth = g₁

acceleration of gravity at the surface of Mars = g₂ = 0.38 g₁

radius of Mars = R₂ = 3400 km

radius of Earth = R₁ = 6400 km

mass of Earth = M₁ = 6 × 10²⁴ kg

Asked:

mass of Mars = M₂ = ?

Solution:

$g_2 = 0.38 g_1$

$G\frac{M_2}{(R_2)^2} = 0.38\ G \frac{M_1}{(R_1)^2}$

$M_2 = 0.38\ (\frac{R_2}{R_1})^2 M_1$

$M_2 = 0.38 \times (\frac{3400}{6400})^2 \times 6 \times 10^{24}$

$M_2 \approx 6.4 \times 10^{23} \texttt{ kg}$

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Conclusion :

Mass of Mars is about 6.4 × 10²³ kg

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Learn more

• Unit of G : https://brainly.com/question/1724648
• Velocity of Runner : https://brainly.com/question/3813437

• Kinetic Energy : https://brainly.com/question/692781

• Acceleration : https://brainly.com/question/2283922

• The Speed of Car : https://brainly.com/question/568302

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Answer details

Grade: High School

Subject: Mathematics

Chapter: Gravitational Force